diff --git a/packages/flutter_tools/lib/src/web/chrome.dart b/packages/flutter_tools/lib/src/web/chrome.dart
index 90af6e5cf8..996d79c468 100644
--- a/packages/flutter_tools/lib/src/web/chrome.dart
+++ b/packages/flutter_tools/lib/src/web/chrome.dart
@@ -507,8 +507,14 @@ class Chromium {
     // Send a command to shut down the browser cleanly.
     Duration sigtermDelay = Duration.zero;
     if (_hasValidChromeConnection) {
-      final ChromeTab? tab = await chromeConnection.getTab(
-          (_) => true, retryFor: const Duration(seconds: 1));
+      ChromeTab? tab;
+      try {
+        tab = await chromeConnection.getTab(
+            (_) => true, retryFor: const Duration(seconds: 1));
+      } on SocketException {
+        // Chrome is not responding to the debug protocol and probably has
+        // already been closed.
+      }
       if (tab != null) {
         final WipConnection wipConnection = await tab.connect();
         await wipConnection.sendCommand('Browser.close');
diff --git a/packages/flutter_tools/test/web.shard/chrome_test.dart b/packages/flutter_tools/test/web.shard/chrome_test.dart
index 08bc8a0502..a7cf10c786 100644
--- a/packages/flutter_tools/test/web.shard/chrome_test.dart
+++ b/packages/flutter_tools/test/web.shard/chrome_test.dart
@@ -820,6 +820,24 @@ void main() {
     await chrome.close();
     expect(commands, contains('Browser.close'));
   });
+
+  test('Chromium close handles a SocketException when connecting to Chrome', () async {
+    final BufferLogger logger = BufferLogger.test();
+    final FakeChromeConnectionWithTab chromeConnection = FakeChromeConnectionWithTab();
+    final ChromiumLauncher chromiumLauncher = ChromiumLauncher(
+      fileSystem: fileSystem,
+      platform: platform,
+      processManager: processManager,
+      operatingSystemUtils: operatingSystemUtils,
+      browserFinder: findChromeExecutable,
+      logger: logger,
+    );
+    final FakeProcess process = FakeProcess();
+    final Chromium chrome = Chromium(0, chromeConnection, chromiumLauncher: chromiumLauncher, process: process, logger: logger);
+    expect(await chromiumLauncher.connect(chrome, false), equals(chrome));
+    chromeConnection.throwSocketExceptions = true;
+    await chrome.close();
+  });
 }
 
 /// Fake chrome connection that fails to get tabs a few times.
@@ -863,14 +881,21 @@ class FakeChromeConnectionWithTab extends Fake implements ChromeConnection {
       : _tab = FakeChromeTab(onSendCommand);
 
   final FakeChromeTab _tab;
+  bool throwSocketExceptions = false;
 
   @override
   Future<ChromeTab?> getTab(bool Function(ChromeTab tab) accept, {Duration? retryFor}) async {
+    if (throwSocketExceptions) {
+      throw const io.SocketException('test');
+    }
     return _tab;
   }
 
   @override
   Future<List<ChromeTab>> getTabs({Duration? retryFor}) async {
+    if (throwSocketExceptions) {
+      throw const io.SocketException('test');
+    }
     return <ChromeTab>[_tab];
   }