diff --git a/changelog.d/7009.feature b/changelog.d/7009.feature
new file mode 100644
index 000000000..cd2705d5b
--- /dev/null
+++ b/changelog.d/7009.feature
@@ -0,0 +1 @@
+Set `Referrer-Policy` header to `no-referrer` on media downloads.
diff --git a/synapse/rest/media/v1/download_resource.py b/synapse/rest/media/v1/download_resource.py
index 66a01559e..24d3ae5bb 100644
--- a/synapse/rest/media/v1/download_resource.py
+++ b/synapse/rest/media/v1/download_resource.py
@@ -50,6 +50,9 @@ class DownloadResource(DirectServeResource):
             b" media-src 'self';"
             b" object-src 'self';",
         )
+        request.setHeader(
+            b"Referrer-Policy", b"no-referrer",
+        )
         server_name, media_id, name = parse_media_id(request)
         if server_name == self.server_name:
             await self.media_repo.get_local_media(request, media_id, name)