diff --git a/qiskit/tools/parallel.py b/qiskit/tools/parallel.py
index 9013b1562c38..ca88c5368234 100644
--- a/qiskit/tools/parallel.py
+++ b/qiskit/tools/parallel.py
@@ -65,6 +65,9 @@
     # Default False on Windows
     if sys.platform == "win32":
         PARALLEL_DEFAULT = False
+    # On python 3.9 default false to avoid deadlock issues
+    elif sys.version_info[0] == 3 and sys.version_info[1] == 9:
+        PARALLEL_DEFAULT = False
     # On macOS default false on Python >=3.8
     elif sys.platform == "darwin":
         if sys.version_info[0] == 3 and sys.version_info[1] >= 8:
diff --git a/releasenotes/notes/disable-39-multirpc-8618c89aeaa620f9.yaml b/releasenotes/notes/disable-39-multirpc-8618c89aeaa620f9.yaml
new file mode 100644
index 000000000000..bfc3e0b16bc0
--- /dev/null
+++ b/releasenotes/notes/disable-39-multirpc-8618c89aeaa620f9.yaml
@@ -0,0 +1,20 @@
+---
+issues:
+  - |
+    When running :func:`~qiskit.tools.parallel_map` (and functions that
+    internally call :func:`~qiskit.tools.parallel_map` such as
+    :func:`~qiskit.compiler.transpile` and :func:`~qiskit.compiler.assemble`)
+    on Python 3.9 with ``QISKIT_PARALLEL`` set to True in some scenarios it is
+    possible for the program to deadlock and never finish running. To avoid
+    this from happening the default for Python 3.9 was changed to not run in
+    parallel, but if ``QISKIT_PARALLEL`` is explicitly enabled then this
+    can still occur.
+upgrade:
+  - |
+    The default value for ``QISKIT_PARALLEL`` on Python 3.9 environments has
+    changed to ``False``, this means that when running on Python 3.9 by default
+    multiprocessing will not be used. This was done to avoid a potential
+    deadlock/hanging issue that can occur when running multiprocessing on
+    Python 3.9 (see the known issues section for more detail). It is still
+    possible to manual enable it by explicitly setting the ``QISKIT_PARALLEL``
+    environment variable to ``TRUE``.