diff --git a/docs/changelog/2797.misc.rst b/docs/changelog/2797.misc.rst
new file mode 100644
index 000000000..dc2a9e04f
--- /dev/null
+++ b/docs/changelog/2797.misc.rst
@@ -0,0 +1,2 @@
+Skip the ``time-machine`` dependency and spinner tests on PyPy because
+it segfaults on this implementation.
diff --git a/pyproject.toml b/pyproject.toml
index 4e2a44b25..e4735d3a1 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -59,7 +59,7 @@ optional-dependencies.testing = [
   "pytest-mock>=3.10",
   "pytest-xdist>=3.1",
   "re-assert>=1.1",
-  "time-machine>=2.8.2",
+  "time-machine>=2.8.2; implementation_name != \"pypy\"",
 ]
 scripts.tox = "tox.run:run"
 dynamic = ["version"]
diff --git a/tests/conftest.py b/tests/conftest.py
index 81c4a4938..b3086268d 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -39,6 +39,12 @@ def _fmt(msg: str) -> str:
     from typing_extensions import Protocol
 
 
+collect_ignore = []
+if sys.implementation.name == "pypy":
+    # time-machine causes segfaults on PyPy
+    collect_ignore.append("util/test_spinner.py")
+
+
 class ToxIniCreator(Protocol):
     def __call__(self, conf: str, override: Sequence[Override] | None = None) -> Config:  # noqa: U100
         ...