diff --git a/browser/components/newtab/lib/FeatureCalloutBroker.sys.mjs b/browser/components/newtab/lib/FeatureCalloutBroker.sys.mjs
index ca2460e8e82b..7bf83d567d89 100644
--- a/browser/components/newtab/lib/FeatureCalloutBroker.sys.mjs
+++ b/browser/components/newtab/lib/FeatureCalloutBroker.sys.mjs
@@ -84,6 +84,13 @@ export class _FeatureCalloutBroker {
       return false;
     }
     const win = browser.ownerGlobal;
+    // Avoid showing feature callouts if a dialog or panel is showing.
+    if (
+      win.gDialogBox?.dialog ||
+      [...win.document.querySelectorAll("panel")].some(p => p.state === "open")
+    ) {
+      return false;
+    }
     const currentCallout = this.#calloutMap.get(win);
     // If a custom callout was previously showing, but is no longer showing,
     // tear down the FeatureCallout instance. We avoid tearing them down when
diff --git a/browser/components/newtab/test/browser/browser_feature_callout_in_chrome.js b/browser/components/newtab/test/browser/browser_feature_callout_in_chrome.js
index 2dd714d648bb..ec9201ecbed0 100644
--- a/browser/components/newtab/test/browser/browser_feature_callout_in_chrome.js
+++ b/browser/components/newtab/test/browser/browser_feature_callout_in_chrome.js
@@ -1,7 +1,9 @@
 /* Any copyright is dedicated to the Public Domain.
  * http://creativecommons.org/publicdomain/zero/1.0/ */
 
-"use strict";
+const { CustomizableUITestUtils } = ChromeUtils.importESModule(
+  "resource://testing-common/CustomizableUITestUtils.sys.mjs"
+);
 
 const PDF_TEST_URL =
   "https://example.com/browser/browser/components/newtab/test/browser/file_pdf.PDF";
@@ -457,6 +459,42 @@ add_task(async function triggered_feature_tour_with_custom_pref() {
   );
 });
 
+add_task(async function callout_not_shown_if_dialog_open() {
+  await SpecialPowers.pushPrefEnv({
+    set: [["prompts.windowPromptSubDialog", true]],
+  });
+
+  const win = await BrowserTestUtils.openNewBrowserWindow();
+  let dialogPromise = BrowserTestUtils.promiseAlertDialogOpen();
+  // Avoid blocking the test on the (sync) alert by sticking it in a timeout:
+  setTimeout(() => Services.prompt.alert(win, "Some title", "some message"), 0);
+  await dialogPromise;
+
+  let rv = await FeatureCalloutBroker.showFeatureCallout(
+    win.gBrowser.selectedBrowser,
+    testMessage.message
+  );
+  ok(!rv, "Feature callout not shown when a dialog is open in the same window");
+
+  await BrowserTestUtils.closeWindow(win);
+  await SpecialPowers.popPrefEnv();
+});
+
+add_task(async function callout_not_shown_if_panel_open() {
+  const win = await BrowserTestUtils.openNewBrowserWindow();
+  const gCUITestUtils = new CustomizableUITestUtils(win);
+  await gCUITestUtils.openMainMenu();
+
+  let rv = await FeatureCalloutBroker.showFeatureCallout(
+    win.gBrowser.selectedBrowser,
+    testMessage.message
+  );
+  ok(!rv, "Feature callout not shown when a panel is open in the same window");
+
+  await gCUITestUtils.hideMainMenu();
+  await BrowserTestUtils.closeWindow(win);
+});
+
 add_task(async function feature_callout_renders_in_browser_chrome_for_pdf() {
   const sandbox = sinon.createSandbox();
   const sendTriggerStub = sandbox.stub(ASRouter, "sendTriggerMessage");