diff --git a/addons/web_editor/static/src/js/editor/snippets.editor.js b/addons/web_editor/static/src/js/editor/snippets.editor.js
index 60a43a2d294..cdbd7c9cbd4 100644
--- a/addons/web_editor/static/src/js/editor/snippets.editor.js
+++ b/addons/web_editor/static/src/js/editor/snippets.editor.js
@@ -2423,7 +2423,7 @@ var SnippetsMenu = Widget.extend({
             $selectorSiblings = $(unique(($selectorSiblings || $()).add($selectorChildren.children()).get()));
         }
 
-        var noDropZonesSelector = '[data-invisible="1"], .o_we_no_overlay, :not(:visible), :not(:o_editable)';
+        var noDropZonesSelector = '[data-invisible="1"], .o_we_no_overlay, :not(:visible)';
         if ($selectorSiblings) {
             $selectorSiblings.not(`.oe_drop_zone, .oe_drop_clone, ${noDropZonesSelector}`).each(function () {
                 var data;
@@ -2835,6 +2835,13 @@ var SnippetsMenu = Widget.extend({
     _computeSelectorFunctions: function (selector, exclude, target, noCheck, isChildren, excludeParent) {
         var self = this;
 
+        // TODO in master: FOR_DROP should be a param of the function.
+        const forDropID = 'FOR_DROP';
+        const forDrop = exclude && exclude.startsWith(forDropID);
+        if (forDrop) {
+            exclude = exclude.substring(forDropID.length);
+        }
+
         // The `:not(.o_editable_media)` part is handled outside of the selector
         // (see filterFunc).
         // Note: the `:not([contenteditable="true"])` part was there for that
@@ -2856,10 +2863,19 @@ var SnippetsMenu = Widget.extend({
                 // When noCheck is true, we only check the exclude.
                 return true;
             }
-            // `o_editable_media` bypasses the `o_not_editable` class.
-            if (this.classList.contains('o_editable_media')) {
+            // `o_editable_media` bypasses the `o_not_editable` class except for
+            // drag & drop.
+            if (!forDrop && this.classList.contains('o_editable_media')) {
                 return weUtils.shouldEditableMediaBeEditable(this);
             }
+            if (forDrop && !isChildren) {
+                // it's a drop-in.
+                return !$(this)
+                    .is('.o_not_editable :not([contenteditable="true"]), .o_not_editable');
+            }
+            if (isChildren) {
+                return !$(this).is('.o_not_editable *');
+            }
             return !$(this)
                 .is('.o_not_editable:not(.s_social_media) :not([contenteditable="true"])');
         };
@@ -2956,8 +2972,8 @@ var SnippetsMenu = Widget.extend({
                 'base_target': target,
                 'selector': self._computeSelectorFunctions(selector, exclude, target, noCheck),
                 '$el': $style,
-                'drop-near': $style.data('drop-near') && self._computeSelectorFunctions($style.data('drop-near'), '', false, noCheck, true, excludeParent),
-                'drop-in': $style.data('drop-in') && self._computeSelectorFunctions($style.data('drop-in'), '', false, noCheck),
+                'drop-near': $style.data('drop-near') && self._computeSelectorFunctions($style.data('drop-near'), 'FOR_DROP', false, noCheck, true, excludeParent),
+                'drop-in': $style.data('drop-in') && self._computeSelectorFunctions($style.data('drop-in'), 'FOR_DROP', false, noCheck),
                 'drop-exclude-ancestor': this.dataset.dropExcludeAncestor,
                 'drop-lock-within': this.dataset.dropLockWithin,
                 'data': Object.assign({string: $style.attr('string')}, $style.data()),
diff --git a/addons/website/static/tests/tours/drag_and_drop_on_non_editable.js b/addons/website/static/tests/tours/drag_and_drop_on_non_editable.js
new file mode 100644
index 00000000000..2c8d3146aee
--- /dev/null
+++ b/addons/website/static/tests/tours/drag_and_drop_on_non_editable.js
@@ -0,0 +1,36 @@
+/** @odoo-module **/
+
+import wTourUtils from '@website/js/tours/tour_utils';
+
+wTourUtils.registerWebsitePreviewTour("test_drag_and_drop_on_non_editable", {
+    test: true,
+    url: "/",
+    edition: true,
+}, () => [
+    wTourUtils.dragNDrop({
+        id: "s_company_team",
+        name: "Team",
+    }),
+    {
+        content: "Click on an editable media in non editable env.",
+        trigger: "iframe .s_company_team .o_not_editable > .o_editable_media",
+    },
+    {
+        content: "Verify that the Replace options is in the editor.",
+        trigger: "we-button[data-replace-media]",
+        isCheck: true,
+    },
+    wTourUtils.goBackToBlocks(),
+    Object.assign(wTourUtils.dragNDrop({
+        id: "s_text_highlight",
+        name: "Text Highlight",
+    }), {
+        content: "Drag and drop the Text Highlight building block next to the Team block media.",
+        run: "drag_and_drop_native iframe .s_company_team .o_not_editable > .o_editable_media",
+    }),
+    {
+        content: "Verify that the Text Highlight building block isn't in a non editable element.",
+        trigger: "iframe .s_company_team :not(.o_not_editable) > .s_text_highlight",
+        isCheck: true,
+    },
+]);
diff --git a/addons/website/tests/test_snippets.py b/addons/website/tests/test_snippets.py
index 75a88b7a563..90fbd71577c 100644
--- a/addons/website/tests/test_snippets.py
+++ b/addons/website/tests/test_snippets.py
@@ -95,3 +95,6 @@ class TestSnippets(HttpCase):
         website.cookies_bar = True
         self.start_tour(self.env['website'].get_client_action_url('/'), 'snippet_popup_and_scrollbar', login='admin')
         self.start_tour(self.env['website'].get_client_action_url('/'), 'snippet_popup_and_animations', login='admin')
+
+    def test_drag_and_drop_on_non_editable(self):
+        self.start_tour(self.env['website'].get_client_action_url('/'), 'test_drag_and_drop_on_non_editable', login='admin')