diff --git a/.github/workflows/master.yml b/.github/workflows/master.yml
index 791a8037e77f3..1b44839f98b03 100644
--- a/.github/workflows/master.yml
+++ b/.github/workflows/master.yml
@@ -102,37 +102,40 @@ jobs:
         java-version: ${{ matrix.java }}
     # PySpark
     - name: Install PyPy3
-      # SQL component also has Python related tests, for example, IntegratedUDFTestUtils.
       # Note that order of Python installations here matters because default python3 is
       # overridden by pypy3.
       uses: actions/setup-python@v2
-      if: contains(matrix.modules, 'pyspark') || (contains(matrix.modules, 'sql') && !contains(matrix.modules, 'sql-'))
+      if: contains(matrix.modules, 'pyspark')
       with:
         python-version: pypy3
         architecture: x64
-    - name: Install Python 3.6
+    - name: Install Python 3.8
       uses: actions/setup-python@v2
-      if: contains(matrix.modules, 'pyspark') || (contains(matrix.modules, 'sql') && !contains(matrix.modules, 'sql-'))
+      if: contains(matrix.modules, 'pyspark')
       with:
-        python-version: 3.6
+        python-version: 3.8
         architecture: x64
     - name: Install Python 2.7
       uses: actions/setup-python@v2
-      if: contains(matrix.modules, 'pyspark') || (contains(matrix.modules, 'sql') && !contains(matrix.modules, 'sql-'))
+      # Yarn has a Python specific test too, for example, YarnClusterSuite.
+      if: contains(matrix.modules, 'yarn') || contains(matrix.modules, 'pyspark') || (contains(matrix.modules, 'sql') && !contains(matrix.modules, 'sql-'))
       with:
         python-version: 2.7
         architecture: x64
-    - name: Install Python packages
-      if: contains(matrix.modules, 'pyspark') || (contains(matrix.modules, 'sql') && !contains(matrix.modules, 'sql-'))
+    - name: Install Python packages (Python 3.8 and PyPy3)
+      if: contains(matrix.modules, 'pyspark')
       # PyArrow is not supported in PyPy yet, see ARROW-2651.
       # TODO(SPARK-32247): scipy installation with PyPy fails for an unknown reason.
       run: |
-        python3 -m pip install numpy "pyarrow==0.14.*" pandas scipy
-        python3 -m pip list
-        python2 -m pip install numpy "pyarrow==0.14.*" pandas scipy
-        python2 -m pip list
+        python3.8 -m pip install numpy "pyarrow==0.14.*" pandas scipy
+        python3.8 -m pip list
         pypy3 -m pip install numpy pandas
         pypy3 -m pip list
+    - name: Install Python packages (Python 2.7)
+      if: contains(matrix.modules, 'pyspark') || (contains(matrix.modules, 'sql') && !contains(matrix.modules, 'sql-'))
+      run: |
+        python2.7 -m pip install numpy "pyarrow==0.14.*" pandas scipy
+        python2.7 -m pip list
     # SparkR
     - name: Install R 3.6
       uses: r-lib/actions/setup-r@v1
diff --git a/python/run-tests.py b/python/run-tests.py
index c34e48aad1211..fdb7a40102079 100755
--- a/python/run-tests.py
+++ b/python/run-tests.py
@@ -160,7 +160,7 @@ def run_individual_python_test(target_dir, test_name, pyspark_python):
 
 
 def get_default_python_executables():
-    python_execs = [x for x in ["python2.7", "python3.6", "pypy"] if which(x)]
+    python_execs = [x for x in ["python2.7", "python3.8", "pypy"] if which(x)]
     if "python2.7" not in python_execs:
         LOGGER.warning("Not testing against `python2.7` because it could not be found; falling"
                        " back to `python` instead")