diff --git a/CHANGELOG.md b/CHANGELOG.md
index f710cf6d6..0c452e703 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -73,6 +73,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 * `include_js()` and `include_css()` now correctly handle file permissions in multi-user settings. (#2061)
 
+* Temporary directories/files created for HTML dependencies will be cleaned up on App object deletion (#2079)
+
 ### Deprecations
 
 * `ui.update_navs()` has been deprecated in favor of `ui.update_navset()`. (#2047)
diff --git a/shiny/_app.py b/shiny/_app.py
index 0de886a69..62d7f8037 100644
--- a/shiny/_app.py
+++ b/shiny/_app.py
@@ -3,6 +3,8 @@
 import copy
 import os
 import secrets
+import shutil
+import tempfile
 from contextlib import AsyncExitStack, asynccontextmanager
 from inspect import signature
 from pathlib import Path
@@ -214,6 +216,35 @@ def __init__(
                 cast("Tag | TagList", ui), lib_prefix=self.lib_prefix
             )
 
+    def __del__(self) -> None:
+        deps = self._registered_dependencies.values()
+        self._cleanup_temp_source_dirs(list(deps))
+
+    @staticmethod
+    def _cleanup_temp_source_dirs(deps: list[HTMLDependency]) -> None:
+        # include_css()/include_js() create temporary directories to hold files that
+        # persist across user sessions, but also need to be cleaned up at some point,
+        # and Python (unlike R) does not cleanup tempdirs on process exit. So, our next
+        # best option is to clean them up when the App object is deleted. It's not
+        # perfect (the App object might be deleted while the process is still running,
+        # and there might be multiple App objects using the same UI). However, it still
+        # seems worth doing since that is such a hypothetical edge case. More generally,
+        # if _any_ HTMLDependency with a source directory that is a _subdirectory_ of
+        # the (system-wide) temp directory, we should remove it.
+        current_temp_dir = os.path.realpath(tempfile.gettempdir())
+        for dep in deps:
+            src = dep.source.get("subdir") if dep.source else None
+            if not src:
+                continue
+            src = os.path.realpath(src)
+            if not os.path.exists(src):
+                continue
+            if src == current_temp_dir:
+                continue
+            common = os.path.commonprefix([src, current_temp_dir])
+            if common == current_temp_dir:
+                shutil.rmtree(src)
+
     def init_starlette_app(self) -> starlette.applications.Starlette:
         routes: list[starlette.routing.BaseRoute] = [
             starlette.routing.WebSocketRoute("/websocket/", self._on_connect_cb),