diff --git a/packages/@aws-cdk/aws-s3-assets/README.md b/packages/@aws-cdk/aws-s3-assets/README.md
index 3d508070d6a50..aab4c46d9c44d 100644
--- a/packages/@aws-cdk/aws-s3-assets/README.md
+++ b/packages/@aws-cdk/aws-s3-assets/README.md
@@ -115,6 +115,7 @@ new assets.Asset(this, 'BundledAsset', {
     },
     // Docker bundling fallback
     image: BundlingDockerImage.fromRegistry('alpine'),
+    entrypoint: ['/bin/sh', '-c'],
     command: ['bundle'],
   },
 });
diff --git a/packages/@aws-cdk/core/lib/bundling.ts b/packages/@aws-cdk/core/lib/bundling.ts
index c9a9c07e77f34..b1247fd913ea0 100644
--- a/packages/@aws-cdk/core/lib/bundling.ts
+++ b/packages/@aws-cdk/core/lib/bundling.ts
@@ -13,6 +13,17 @@ export interface BundlingOptions {
    */
   readonly image: BundlingDockerImage;
 
+  /**
+   * The entrypoint to run in the Docker container.
+   *
+   * @example ['/bin/sh', '-c']
+   *
+   * @see https://docs.docker.com/engine/reference/builder/#entrypoint
+   *
+   * @default - run the entrypoint defined in the image
+   */
+  readonly entrypoint?: string[];
+
   /**
    * The command to run in the Docker container.
    *
@@ -152,7 +163,15 @@ export class BundlingDockerImage {
   public run(options: DockerRunOptions = {}) {
     const volumes = options.volumes || [];
     const environment = options.environment || {};
-    const command = options.command || [];
+    const entrypoint = options.entrypoint?.[0] || null;
+    const command = [
+      ...options.entrypoint?.[1]
+        ? [...options.entrypoint.slice(1)]
+        : [],
+      ...options.command
+        ? [...options.command]
+        : [],
+    ];
 
     const dockerArgs: string[] = [
       'run', '--rm',
@@ -164,6 +183,9 @@ export class BundlingDockerImage {
       ...options.workingDirectory
         ? ['-w', options.workingDirectory]
         : [],
+      ...entrypoint
+        ? ['--entrypoint', entrypoint]
+        : [],
       this.image,
       ...command,
     ];
@@ -238,6 +260,13 @@ export enum DockerVolumeConsistency {
  * Docker run options
  */
 export interface DockerRunOptions {
+  /**
+   * The entrypoint to run in the container.
+   *
+   * @default - run the entrypoint defined in the image
+   */
+  readonly entrypoint?: string[];
+
   /**
    * The command to run in the container.
    *
diff --git a/packages/@aws-cdk/core/test/bundling.test.ts b/packages/@aws-cdk/core/test/bundling.test.ts
index e2b0d6b43b98b..258860d65585c 100644
--- a/packages/@aws-cdk/core/test/bundling.test.ts
+++ b/packages/@aws-cdk/core/test/bundling.test.ts
@@ -171,6 +171,44 @@ nodeunitShim({
     test.done();
   },
 
+  'custom entrypoint is passed through to docker exec'(test: Test) {
+    const spawnSyncStub = sinon.stub(child_process, 'spawnSync').returns({
+      status: 0,
+      stderr: Buffer.from('stderr'),
+      stdout: Buffer.from('stdout'),
+      pid: 123,
+      output: ['stdout', 'stderr'],
+      signal: null,
+    });
+
+    const image = BundlingDockerImage.fromRegistry('alpine');
+    image.run({
+      entrypoint: ['/cool/entrypoint', '--cool-entrypoint-arg'],
+      command: ['cool', 'command'],
+      environment: {
+        VAR1: 'value1',
+        VAR2: 'value2',
+      },
+      volumes: [{ hostPath: '/host-path', containerPath: '/container-path' }],
+      workingDirectory: '/working-directory',
+      user: 'user:group',
+    });
+
+    test.ok(spawnSyncStub.calledWith('docker', [
+      'run', '--rm',
+      '-u', 'user:group',
+      '-v', '/host-path:/container-path:delegated',
+      '--env', 'VAR1=value1',
+      '--env', 'VAR2=value2',
+      '-w', '/working-directory',
+      '--entrypoint', '/cool/entrypoint',
+      'alpine',
+      '--cool-entrypoint-arg',
+      'cool', 'command',
+    ], { stdio: ['ignore', process.stderr, 'inherit'] }));
+    test.done();
+  },
+
   'cp utility copies from an image'(test: Test) {
     // GIVEN
     const containerId = '1234567890abcdef1234567890abcdef';