diff --git a/.github/workflows/unit-tests.yml b/.github/workflows/unit-tests.yml
index 69baa3ccd6f34f..553d3e7d568a17 100644
--- a/.github/workflows/unit-tests.yml
+++ b/.github/workflows/unit-tests.yml
@@ -241,6 +241,49 @@ jobs:
       group: ${{ github.event_name == 'push' && github.run_number || github.ref }}-32bit
       cancel-in-progress: true
 
+  Linux-Musl:
+    runs-on: ubuntu-22.04
+    container:
+      image: quay.io/pypa/musllinux_1_1_x86_64
+    steps:
+      - name: Checkout pandas Repo
+        # actions/checkout does not work since it requires node
+        run: |
+          git config --global --add safe.directory $PWD
+
+          if [ $GITHUB_EVENT_NAME != pull_request ]; then
+              git clone --recursive --branch=$GITHUB_REF_NAME https://github.com/${GITHUB_REPOSITORY}.git $GITHUB_WORKSPACE
+              git reset --hard $GITHUB_SHA
+          else
+              git clone --recursive https://github.com/${GITHUB_REPOSITORY}.git $GITHUB_WORKSPACE
+              git fetch origin $GITHUB_REF:my_ref_name
+              git checkout $GITHUB_BASE_REF
+              git -c user.email="you@example.com" merge --no-commit my_ref_name
+          fi
+      - name: Configure System Packages
+        run: |
+          apk update
+          apk add musl-locales
+      - name: Build environment
+        run: |
+          /opt/python/cp39-cp39/bin/python -m venv ~/virtualenvs/pandas-dev
+          . ~/virtualenvs/pandas-dev/bin/activate
+          python -m pip install --no-cache-dir --no-deps -U pip wheel setuptools
+          python -m pip install --no-cache-dir versioneer[toml] cython numpy python-dateutil pytz pytest>=7.0.0 pytest-xdist>=2.2.0 pytest-asyncio>=0.17 hypothesis>=6.46.1
+          python setup.py build_ext -q -j$(nproc)
+          python -m pip install --no-cache-dir --no-build-isolation --no-use-pep517 -e .
+          python -m pip list --no-cache-dir
+
+      - name: Run Tests
+        run: |
+          . ~/virtualenvs/pandas-dev/bin/activate
+          export PANDAS_CI=1
+          python -m pytest -m 'not slow and not network and not clipboard and not single_cpu' pandas --junitxml=test-data.xml
+    concurrency:
+      # https://github.community/t/concurrecy-not-work-for-push/183068/7
+      group: ${{ github.event_name == 'push' && github.run_number || github.ref }}-musl
+      cancel-in-progress: true
+
   python-dev:
     # This job may or may not run depending on the state of the next
     # unreleased Python version. DO NOT DELETE IT.
diff --git a/pandas/compat/__init__.py b/pandas/compat/__init__.py
index 3d7589bf67ee2a..00957c45a7fbeb 100644
--- a/pandas/compat/__init__.py
+++ b/pandas/compat/__init__.py
@@ -16,6 +16,7 @@
 
 from pandas.compat._constants import (
     IS64,
+    ISMUSL,
     PY310,
     PY311,
     PYPY,
@@ -160,6 +161,7 @@ def get_lzma_file() -> type[pandas.compat.compressors.LZMAFile]:
     "pa_version_under9p0",
     "pa_version_under11p0",
     "IS64",
+    "ISMUSL",
     "PY310",
     "PY311",
     "PYPY",
diff --git a/pandas/compat/_constants.py b/pandas/compat/_constants.py
index 1d522a5b4cd09f..1d7fe23b3d2ea9 100644
--- a/pandas/compat/_constants.py
+++ b/pandas/compat/_constants.py
@@ -9,16 +9,19 @@
 
 import platform
 import sys
+import sysconfig
 
 IS64 = sys.maxsize > 2**32
 
 PY310 = sys.version_info >= (3, 10)
 PY311 = sys.version_info >= (3, 11)
 PYPY = platform.python_implementation() == "PyPy"
+ISMUSL = "musl" in (sysconfig.get_config_var("HOST_GNU_TYPE") or "")
 
 
 __all__ = [
     "IS64",
+    "ISMUSL",
     "PY310",
     "PY311",
     "PYPY",
diff --git a/pandas/tests/config/test_localization.py b/pandas/tests/config/test_localization.py
index 6474177261b919..3907f557d10755 100644
--- a/pandas/tests/config/test_localization.py
+++ b/pandas/tests/config/test_localization.py
@@ -10,6 +10,8 @@
     set_locale,
 )
 
+from pandas.compat import ISMUSL
+
 import pandas as pd
 
 _all_locales = get_locales()
@@ -46,7 +48,19 @@ def test_can_set_locale_valid_set(lc_var):
     assert before_locale == after_locale
 
 
-@pytest.mark.parametrize("lc_var", (locale.LC_ALL, locale.LC_CTYPE, locale.LC_TIME))
+@pytest.mark.parametrize(
+    "lc_var",
+    (
+        locale.LC_ALL,
+        locale.LC_CTYPE,
+        pytest.param(
+            locale.LC_TIME,
+            marks=pytest.mark.skipif(
+                ISMUSL, reason="MUSL allows setting invalid LC_TIME."
+            ),
+        ),
+    ),
+)
 def test_can_set_locale_invalid_set(lc_var):
     # Cannot set an invalid locale.
     before_locale = _get_current_locale(lc_var)
diff --git a/pandas/tests/tslibs/test_parsing.py b/pandas/tests/tslibs/test_parsing.py
index 6500afdf87beb4..587527c2058d7b 100644
--- a/pandas/tests/tslibs/test_parsing.py
+++ b/pandas/tests/tslibs/test_parsing.py
@@ -14,12 +14,19 @@
     strptime,
 )
 from pandas._libs.tslibs.parsing import parse_datetime_string_with_reso
+from pandas.compat import (
+    ISMUSL,
+    is_platform_windows,
+)
 import pandas.util._test_decorators as td
 
 import pandas._testing as tm
 
 
-@td.skip_if_windows
+@pytest.mark.skipif(
+    is_platform_windows() or ISMUSL,
+    reason="TZ setting incorrect on Windows and MUSL Linux",
+)
 def test_parsing_tzlocal_deprecated():
     # GH#50791
     msg = "Pass the 'tz' keyword or call tz_localize after construction instead"