diff --git a/CHANGELOG.md b/CHANGELOG.md
index 58e84af5e2..ca0ad9520c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,10 @@ and this project adheres to [Semantic Versioning](http://semver.org/).
 
 ## [6.1.0] - 2025-08-01
 
+### Fixed
+
+- Fixed `Markdown` and `MarkdownViewer` widgets both handling `Markdown.LinkClicked` messages https://github.com/Textualize/textual/pull/6093
+
 ### Added
 
 - Added `Button.flat` boolean to enable flat button style https://github.com/Textualize/textual/pull/6094
diff --git a/src/textual/widgets/_markdown.py b/src/textual/widgets/_markdown.py
index 397b265b50..0bc4c283de 100644
--- a/src/textual/widgets/_markdown.py
+++ b/src/textual/widgets/_markdown.py
@@ -6,7 +6,7 @@
 from functools import partial
 from pathlib import Path, PurePath
 from typing import Callable, Iterable, Optional
-from urllib.parse import unquote
+from urllib.parse import unquote, urlparse
 
 from markdown_it import MarkdownIt
 from markdown_it.token import Token
@@ -1128,8 +1128,9 @@ async def stream_markdown(self) -> None:
         return updater
 
     def on_markdown_link_clicked(self, event: LinkClicked) -> None:
-        if self._open_links:
+        if self._open_links and is_http_url(event.href):
             self.app.open_url(event.href)
+            event.stop()
 
     @staticmethod
     def sanitize_location(location: str) -> tuple[Path, str]:
@@ -1628,8 +1629,9 @@ async def forward(self) -> None:
             self.post_message(self.NavigatorUpdated())
 
     async def _on_markdown_link_clicked(self, message: Markdown.LinkClicked) -> None:
-        message.stop()
-        await self.go(message.href)
+        if not is_http_url(message.href):
+            message.stop()
+            await self.go(message.href)
 
     def watch_show_table_of_contents(self, show_table_of_contents: bool) -> None:
         self.set_class(show_table_of_contents, "-show-table-of-contents")
@@ -1657,3 +1659,9 @@ def _on_markdown_table_of_contents_selected(
         block = self.query_one(block_selector, MarkdownBlock)
         self.scroll_to_widget(block, top=True)
         message.stop()
+
+
+def is_http_url(url: str) -> bool:
+    """Check if a URL is an HTTP or HTTPS URL."""
+    parsed = urlparse(url)
+    return parsed.scheme in ("http", "https")
diff --git a/tests/test_markdownviewer.py b/tests/test_markdownviewer.py
index 3c83d271d2..85075b1ae7 100644
--- a/tests/test_markdownviewer.py
+++ b/tests/test_markdownviewer.py
@@ -12,6 +12,7 @@
 TEST_MARKDOWN = """\
 * [First]({{file}}#first)
 * [Second](#second)
+* [GitHub](https://github.com/textualize/textual/)
 
 # First
 
@@ -24,6 +25,7 @@
 
 
 class MarkdownFileViewerApp(App[None]):
+
     def __init__(self, markdown_file: Path) -> None:
         super().__init__()
         self.markdown_file = markdown_file
@@ -37,14 +39,14 @@ async def on_mount(self) -> None:
         await self.query_one(MarkdownViewer).go(self.markdown_file)
 
 
-@pytest.mark.parametrize("link", [0, 1])
+@pytest.mark.parametrize("link", [0, 1, 2])
 async def test_markdown_file_viewer_anchor_link(tmp_path, link: int) -> None:
     """Test https://github.com/Textualize/textual/issues/3094"""
     async with MarkdownFileViewerApp(Path(tmp_path) / "test.md").run_test() as pilot:
         # There's not really anything to test *for* here, but the lack of an
         # exception is the win (before the fix this is testing it would have
         # been FileNotFoundError).
-        await pilot.click(Markdown, Offset(2, link))
+        await pilot.click(Markdown, Offset(4, link))
 
 
 class MarkdownStringViewerApp(App[None]):
@@ -59,7 +61,7 @@ async def on_mount(self) -> None:
         self.query_one(MarkdownViewer).show_table_of_contents = False
 
 
-@pytest.mark.parametrize("link", [0, 1])
+@pytest.mark.parametrize("link", [0, 1, 2])
 async def test_markdown_string_viewer_anchor_link(link: int) -> None:
     """Test https://github.com/Textualize/textual/issues/3094
 
@@ -70,7 +72,7 @@ async def test_markdown_string_viewer_anchor_link(link: int) -> None:
         # There's not really anything to test *for* here, but the lack of an
         # exception is the win (before the fix this is testing it would have
         # been FileNotFoundError).
-        await pilot.click(Markdown, Offset(2, link))
+        await pilot.click(Markdown, Offset(4, link))
 
 
 @pytest.mark.parametrize("text", ["Hey [[/test]]", "[i]Hey there[/i]"])