diff --git a/src/browser/setupWorker/glossary.ts b/src/browser/setupWorker/glossary.ts
index 084f3cc65..23017c6ec 100644
--- a/src/browser/setupWorker/glossary.ts
+++ b/src/browser/setupWorker/glossary.ts
@@ -72,7 +72,7 @@ export type ServiceWorkerOutgoingEventTypes =
   | 'CLIENT_CLOSED'
 
 export interface StringifiedResponse extends ResponseInit {
-  body: string | ReadableStream<Uint8Array> | null
+  body: string | ArrayBuffer | ReadableStream<Uint8Array> | null
 }
 
 /**
@@ -146,7 +146,10 @@ export interface SetupWorkerInternalContext {
       ServiceWorkerMessage<EventType, ServiceWorkerIncomingEventsMap[EventType]>
     >
   }
-  useFallbackMode: boolean
+  supports: {
+    serviceWorkerApi: boolean
+    readableStreamTransfer: boolean
+  }
   fallbackInterceptor?: Interceptor<HttpRequestEventMap>
 }
 
diff --git a/src/browser/setupWorker/setupWorker.ts b/src/browser/setupWorker/setupWorker.ts
index 301e4e520..b89376641 100644
--- a/src/browser/setupWorker/setupWorker.ts
+++ b/src/browser/setupWorker/setupWorker.ts
@@ -20,6 +20,7 @@ import { SetupApi } from '~/core/SetupApi'
 import { mergeRight } from '~/core/utils/internal/mergeRight'
 import { LifeCycleEventsMap } from '~/core/sharedOptions'
 import { SetupWorker } from './glossary'
+import { supportsReadableStreamTransfer } from '../utils/supportsReadableStreamTransfer'
 
 interface Listener {
   target: EventTarget
@@ -142,8 +143,11 @@ export class SetupWorkerApi
           })
         },
       },
-      useFallbackMode:
-        !('serviceWorker' in navigator) || location.protocol === 'file:',
+      supports: {
+        serviceWorkerApi:
+          !('serviceWorker' in navigator) || location.protocol === 'file:',
+        readableStreamTransfer: supportsReadableStreamTransfer(),
+      },
     }
 
     /**
@@ -156,11 +160,11 @@ export class SetupWorkerApi
       },
     })
 
-    this.startHandler = context.useFallbackMode
+    this.startHandler = context.supports.serviceWorkerApi
       ? createFallbackStart(context)
       : createStartHandler(context)
 
-    this.stopHandler = context.useFallbackMode
+    this.stopHandler = context.supports.serviceWorkerApi
       ? createFallbackStop(context)
       : createStop(context)
 
diff --git a/src/browser/setupWorker/start/createRequestListener.ts b/src/browser/setupWorker/start/createRequestListener.ts
index dccd989de..b6ee1e56a 100644
--- a/src/browser/setupWorker/start/createRequestListener.ts
+++ b/src/browser/setupWorker/start/createRequestListener.ts
@@ -47,18 +47,29 @@ export const createRequestListener = (
             // ".log()" method of the request handler.
             const responseClone = response.clone()
             const responseInit = toResponseInit(response)
-            const responseStream = responseClone.body
 
-            messageChannel.postMessage(
-              'MOCK_RESPONSE',
-              {
+            /**
+             * @note Safari doesn't support transferring a "ReadableStream".
+             * Check that the browser supports that before sending it to the worker.
+             */
+            if (context.supports.readableStreamTransfer) {
+              const responseStream = response.body
+              messageChannel.postMessage(
+                'MOCK_RESPONSE',
+                {
+                  ...responseInit,
+                  body: responseStream,
+                },
+                responseStream ? [responseStream] : undefined,
+              )
+            } else {
+              // As a fallback, send the response body buffer to the worker.
+              const responseBuffer = await responseClone.arrayBuffer()
+              messageChannel.postMessage('MOCK_RESPONSE', {
                 ...responseInit,
-                body: responseStream,
-              },
-              // Transfer response's buffer so it could
-              // be sent over to the worker.
-              responseStream ? [responseStream] : undefined,
-            )
+                body: responseBuffer,
+              })
+            }
 
             if (!options.quiet) {
               context.emitter.once('response:mocked', ({ response }) => {
diff --git a/src/browser/utils/supportsReadableStreamTransfer.ts b/src/browser/utils/supportsReadableStreamTransfer.ts
new file mode 100644
index 000000000..b1c5dc295
--- /dev/null
+++ b/src/browser/utils/supportsReadableStreamTransfer.ts
@@ -0,0 +1,17 @@
+/**
+ * Returns a boolean indicating whether the current browser
+ * supports `ReadableStream` as a `Transferable` when posting
+ * messages.
+ */
+export function supportsReadableStreamTransfer() {
+  try {
+    const stream = new ReadableStream({
+      start: (controller) => controller.close(),
+    })
+    const message = new MessageChannel()
+    message.port1.postMessage(stream, [stream])
+    return true
+  } catch (error) {
+    return false
+  }
+}