diff --git a/packages/babel-parser/src/plugins/typescript.js b/packages/babel-parser/src/plugins/typescript.js
index c23fd5d3c6..72aa5c4b9e 100644
--- a/packages/babel-parser/src/plugins/typescript.js
+++ b/packages/babel-parser/src/plugins/typescript.js
@@ -342,17 +342,18 @@ export default (superClass: Class<Parser>): Class<Parser> =>
     }
 
     tsParseBindingListForSignature(): $ReadOnlyArray<
-      N.Identifier | N.RestElement | N.ObjectPattern,
+      N.Identifier | N.RestElement | N.ObjectPattern | N.ArrayPattern,
     > {
       return this.parseBindingList(tt.parenR).map(pattern => {
         if (
           pattern.type !== "Identifier" &&
           pattern.type !== "RestElement" &&
-          pattern.type !== "ObjectPattern"
+          pattern.type !== "ObjectPattern" &&
+          pattern.type !== "ArrayPattern"
         ) {
           throw this.unexpected(
             pattern.start,
-            `Name in a signature must be an Identifier or ObjectPattern, instead got ${
+            `Name in a signature must be an Identifier, ObjectPattern or ArrayPattern, instead got ${
               pattern.type
             }`,
           );
@@ -794,6 +795,21 @@ export default (superClass: Class<Parser>): Class<Parser> =>
         return true;
       }
 
+      if (this.match(tt.bracketL)) {
+        let braceStackCounter = 1;
+        this.next();
+
+        while (braceStackCounter > 0) {
+          if (this.match(tt.bracketL)) {
+            ++braceStackCounter;
+          } else if (this.match(tt.bracketR)) {
+            --braceStackCounter;
+          }
+          this.next();
+        }
+        return true;
+      }
+
       return false;
     }
 
diff --git a/packages/babel-parser/src/types.js b/packages/babel-parser/src/types.js
index f00eb1be27..06e5a03a71 100644
--- a/packages/babel-parser/src/types.js
+++ b/packages/babel-parser/src/types.js
@@ -1076,7 +1076,9 @@ export type TsSignatureDeclaration =
 
 export type TsSignatureDeclarationOrIndexSignatureBase = NodeBase & {
   // Not using TypeScript's "ParameterDeclaration" here, since it's inconsistent with regular functions.
-  parameters: $ReadOnlyArray<Identifier | RestElement | ObjectPattern>,
+  parameters: $ReadOnlyArray<
+    Identifier | RestElement | ObjectPattern | ArrayPattern,
+  >,
   typeAnnotation: ?TsTypeAnnotation,
 };
 
diff --git a/packages/babel-parser/test/fixtures/typescript/regression/destructuring-in-function-type/input.js b/packages/babel-parser/test/fixtures/typescript/regression/destructuring-in-function-type/input.js
index 8b22756932..56f3b25d96 100644
--- a/packages/babel-parser/test/fixtures/typescript/regression/destructuring-in-function-type/input.js
+++ b/packages/babel-parser/test/fixtures/typescript/regression/destructuring-in-function-type/input.js
@@ -1 +1,3 @@
 type MyType = ({ theme }: any) => any
+
+type AnotherType = ([a]: any) => any
diff --git a/packages/babel-parser/test/fixtures/typescript/regression/destructuring-in-function-type/output.json b/packages/babel-parser/test/fixtures/typescript/regression/destructuring-in-function-type/output.json
index c93fa7945f..38916a8426 100644
--- a/packages/babel-parser/test/fixtures/typescript/regression/destructuring-in-function-type/output.json
+++ b/packages/babel-parser/test/fixtures/typescript/regression/destructuring-in-function-type/output.json
@@ -1,29 +1,29 @@
 {
   "type": "File",
   "start": 0,
-  "end": 37,
+  "end": 75,
   "loc": {
     "start": {
       "line": 1,
       "column": 0
     },
     "end": {
-      "line": 1,
-      "column": 37
+      "line": 3,
+      "column": 36
     }
   },
   "program": {
     "type": "Program",
     "start": 0,
-    "end": 37,
+    "end": 75,
     "loc": {
       "start": {
         "line": 1,
         "column": 0
       },
       "end": {
-        "line": 1,
-        "column": 37
+        "line": 3,
+        "column": 36
       }
     },
     "sourceType": "module",
@@ -209,6 +209,149 @@
             }
           }
         }
+      },
+      {
+        "type": "TSTypeAliasDeclaration",
+        "start": 39,
+        "end": 75,
+        "loc": {
+          "start": {
+            "line": 3,
+            "column": 0
+          },
+          "end": {
+            "line": 3,
+            "column": 36
+          }
+        },
+        "id": {
+          "type": "Identifier",
+          "start": 44,
+          "end": 55,
+          "loc": {
+            "start": {
+              "line": 3,
+              "column": 5
+            },
+            "end": {
+              "line": 3,
+              "column": 16
+            },
+            "identifierName": "AnotherType"
+          },
+          "name": "AnotherType"
+        },
+        "typeAnnotation": {
+          "type": "TSFunctionType",
+          "start": 58,
+          "end": 75,
+          "loc": {
+            "start": {
+              "line": 3,
+              "column": 19
+            },
+            "end": {
+              "line": 3,
+              "column": 36
+            }
+          },
+          "parameters": [
+            {
+              "type": "ArrayPattern",
+              "start": 59,
+              "end": 67,
+              "loc": {
+                "start": {
+                  "line": 3,
+                  "column": 20
+                },
+                "end": {
+                  "line": 3,
+                  "column": 28
+                }
+              },
+              "elements": [
+                {
+                  "type": "Identifier",
+                  "start": 60,
+                  "end": 61,
+                  "loc": {
+                    "start": {
+                      "line": 3,
+                      "column": 21
+                    },
+                    "end": {
+                      "line": 3,
+                      "column": 22
+                    },
+                    "identifierName": "a"
+                  },
+                  "name": "a"
+                }
+              ],
+              "typeAnnotation": {
+                "type": "TSTypeAnnotation",
+                "start": 62,
+                "end": 67,
+                "loc": {
+                  "start": {
+                    "line": 3,
+                    "column": 23
+                  },
+                  "end": {
+                    "line": 3,
+                    "column": 28
+                  }
+                },
+                "typeAnnotation": {
+                  "type": "TSAnyKeyword",
+                  "start": 64,
+                  "end": 67,
+                  "loc": {
+                    "start": {
+                      "line": 3,
+                      "column": 25
+                    },
+                    "end": {
+                      "line": 3,
+                      "column": 28
+                    }
+                  }
+                }
+              }
+            }
+          ],
+          "typeAnnotation": {
+            "type": "TSTypeAnnotation",
+            "start": 69,
+            "end": 75,
+            "loc": {
+              "start": {
+                "line": 3,
+                "column": 30
+              },
+              "end": {
+                "line": 3,
+                "column": 36
+              }
+            },
+            "typeAnnotation": {
+              "type": "TSAnyKeyword",
+              "start": 72,
+              "end": 75,
+              "loc": {
+                "start": {
+                  "line": 3,
+                  "column": 33
+                },
+                "end": {
+                  "line": 3,
+                  "column": 36
+                }
+              }
+            }
+          }
+        }
       }
     ],
     "directives": []