diff --git a/CHANGELOG.md b/CHANGELOG.md
index bc994dad74fda..4d95ed89c4daa 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,6 +2,12 @@
 
 All notable changes to this project will be documented in this file. See [standard-version](https://github.com/conventional-changelog/standard-version) for commit guidelines.
 
+## [1.49.1](https://github.com/aws/aws-cdk/compare/v1.49.0...v1.49.1) (2020-07-02)
+
+### Bug Fixes
+
+* **apigateway:** Lambda integration for imported functions ([#8870](https://github.com/aws/aws-cdk/issues/8870)) ([c017f88](https://github.com/aws/aws-cdk/commit/c017f887770174437de3b772edf0034604890ac3)), closes [#8869](https://github.com/aws/aws-cdk/issues/8869)
+
 ## [1.49.0](https://github.com/aws/aws-cdk/compare/v1.48.0...v1.49.0) (2020-07-02)
 
 
diff --git a/lerna.json b/lerna.json
index 0c9388ceb22ac..2babe6847f5c3 100644
--- a/lerna.json
+++ b/lerna.json
@@ -10,5 +10,5 @@
     "tools/*"
   ],
   "rejectCycles": "true",
-  "version": "1.49.0"
+  "version": "1.49.1"
 }
diff --git a/packages/@aws-cdk/aws-apigateway/lib/integrations/lambda.ts b/packages/@aws-cdk/aws-apigateway/lib/integrations/lambda.ts
index 715c1d91237fe..60283b75d2fad 100644
--- a/packages/@aws-cdk/aws-apigateway/lib/integrations/lambda.ts
+++ b/packages/@aws-cdk/aws-apigateway/lib/integrations/lambda.ts
@@ -73,10 +73,20 @@ export class LambdaIntegration extends AwsIntegration {
       });
     }
 
-    const cfnFunction = this.handler.node.defaultChild as lambda.CfnFunction;
+    let functionName;
+
+    if (this.handler instanceof lambda.Function) {
+      // if not imported, extract the name from the CFN layer to reach
+      // the literal value if it is given (rather than a token)
+      functionName = (this.handler.node.defaultChild as lambda.CfnFunction).functionName;
+    } else {
+      // imported, just take the function name.
+      functionName = this.handler.functionName;
+    }
+
     let deploymentToken;
-    if (!Token.isUnresolved(cfnFunction.functionName)) {
-      deploymentToken = JSON.stringify({ functionName: cfnFunction.functionName });
+    if (!Token.isUnresolved(functionName)) {
+      deploymentToken = JSON.stringify({ functionName });
     }
     return {
       deploymentToken,
diff --git a/packages/@aws-cdk/aws-apigateway/test/test.lambda.ts b/packages/@aws-cdk/aws-apigateway/test/test.lambda.ts
index afc1a2230e848..b518db5a29bc9 100644
--- a/packages/@aws-cdk/aws-apigateway/test/test.lambda.ts
+++ b/packages/@aws-cdk/aws-apigateway/test/test.lambda.ts
@@ -259,4 +259,23 @@ export = {
 
     test.done();
   },
+
+  'bind works for integration with imported functions'(test: Test) {
+    // GIVEN
+    const stack = new cdk.Stack();
+    const restapi = new apigateway.RestApi(stack, 'RestApi');
+    const method = restapi.root.addMethod('ANY');
+    const handler = lambda.Function.fromFunctionArn(stack, 'MyFunc', 'arn:aws:lambda:region:account:function:myfunc');
+    const integration = new apigateway.LambdaIntegration(handler);
+
+    // WHEN
+    const bindResult = integration.bind(method);
+
+    // the deployment token should be defined since the function name
+    // should be a literal string.
+    test.equal(bindResult?.deploymentToken, JSON.stringify({functionName: 'myfunc'}));
+
+    test.done();
+  },
+
 };