diff --git a/CHANGES.rst b/CHANGES.rst
index 5019208e4..65828cedb 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -9,6 +9,8 @@ Unreleased
 -   Use modern packaging metadata with ``pyproject.toml`` instead of ``setup.cfg``.
     :pr:`1793`
 -   Use ``flit_core`` instead of ``setuptools`` as build backend.
+-   Add support for ``pathlib.Path`` and ``os.Pathlike`` objects to
+    ``TemplateStream.dump``. :issue:`2039`
 
 
 Version 3.1.5
diff --git a/src/jinja2/environment.py b/src/jinja2/environment.py
index a99cc2d1d..533350478 100644
--- a/src/jinja2/environment.py
+++ b/src/jinja2/environment.py
@@ -61,6 +61,8 @@
     from .ext import Extension
     from .loaders import BaseLoader
 
+    StrOrBytesPath = t.Union[str, bytes, "os.PathLike[str]", "os.PathLike[bytes]"]
+
 _env_bound = t.TypeVar("_env_bound", bound="Environment")
 
 
@@ -1592,7 +1594,7 @@ def __init__(self, gen: t.Iterator[str]) -> None:
 
     def dump(
         self,
-        fp: t.Union[str, t.IO[bytes]],
+        fp: t.Union["StrOrBytesPath", t.IO[bytes]],
         encoding: t.Optional[str] = None,
         errors: t.Optional[str] = "strict",
     ) -> None:
@@ -1604,17 +1606,20 @@ def dump(
 
             Template('Hello {{ name }}!').stream(name='foo').dump('hello.html')
         """
+        real_fp: t.IO[bytes]
+
         close = False
 
-        if isinstance(fp, str):
+        try:
+            real_fp = open(fp, "wb")  # type: ignore[arg-type]
+        except TypeError:
+            real_fp = fp  # type: ignore[assignment]
+        else:
+            close = True
+
             if encoding is None:
                 encoding = "utf-8"
 
-            real_fp: t.IO[bytes] = open(fp, "wb")
-            close = True
-        else:
-            real_fp = fp
-
         try:
             if encoding is not None:
                 iterable = (x.encode(encoding, errors) for x in self)  # type: ignore
@@ -1623,9 +1628,15 @@ def dump(
 
             if hasattr(real_fp, "writelines"):
                 real_fp.writelines(iterable)
-            else:
+            elif hasattr(real_fp, "write"):
                 for item in iterable:
                     real_fp.write(item)
+            else:
+                raise AttributeError(
+                    f"'{real_fp.__class__.__name__}' object has no attribute"
+                    f" 'write' or 'writelines'"
+                )
+
         finally:
             if close:
                 real_fp.close()
diff --git a/tests/test_api.py b/tests/test_api.py
index 4472b85ac..9b2d61b3f 100644
--- a/tests/test_api.py
+++ b/tests/test_api.py
@@ -1,5 +1,8 @@
+import io
+import os
 import shutil
 import tempfile
+import typing as t
 from pathlib import Path
 
 import pytest
@@ -242,16 +245,54 @@ def test_streaming_behavior(self, env):
         stream.disable_buffering()
         assert not stream.buffered
 
-    def test_dump_stream(self, env):
+
+class TestStreamingDump:
+    class CustomPathLike:
+        def __init__(self, path: Path):
+            self._path = path
+
+        def __fspath__(self):
+            return self._path.__fspath__()
+
+    class CustomWithWrite:
+        def __init__(self):
+            self._value = []
+
+        def write(self, value: bytes) -> None:
+            self._value.append(value)
+
+        def getvalue(self) -> bytes:
+            return b"".join(self._value)
+
+    class CustomWithWriteLines:
+        def __init__(self):
+            self._value = []
+
+        def writelines(self, value: t.Iterable[bytes]) -> None:
+            self._value += list(value)
+
+        def getvalue(self) -> bytes:
+            return b"".join(self._value)
+
+    @pytest.mark.parametrize("cast_to", [str, Path, os.fspath, CustomPathLike, bytes])
+    def test_dump_stream_file_path(self, env, cast_to):
         tmp = Path(tempfile.mkdtemp())
         try:
             tmpl = env.from_string("\u2713")
             stream = tmpl.stream()
-            stream.dump(str(tmp / "dump.txt"), "utf-8")
+            stream.dump(cast_to(tmp / "dump.txt"), "utf-8")
             assert (tmp / "dump.txt").read_bytes() == b"\xe2\x9c\x93"
         finally:
             shutil.rmtree(tmp)
 
+    @pytest.mark.parametrize("obj", [io.BytesIO, CustomWithWrite, CustomWithWriteLines])
+    def test_dump_stream_io(self, env, obj):
+        tmpl = env.from_string("\u2713")
+        stream = tmpl.stream()
+        _io = obj()
+        stream.dump(_io, "utf-8")
+        assert _io.getvalue() == b"\xe2\x9c\x93"
+
 
 class TestUndefined:
     def test_stopiteration_is_undefined(self):