diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 652366de5b..69ccac5e64 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -28,7 +28,7 @@ stages:
       variables:
         python.version: '3.7'
         CIBW_BEFORE_BUILD: pip install -U Cython
-        CIBW_SKIP: cp27-* cp34-* cp35-* pp*
+        CIBW_SKIP: cp27-* cp34-* cp35-* cp36-* pp*
         TWINE_USERNAME: qiskit
         CIBW_TEST_COMMAND: python {project}/examples/python/stochastic_swap.py
       steps:
@@ -72,7 +72,7 @@ stages:
       variables:
         python.version: '3.7'
         CIBW_BEFORE_BUILD: pip install -U Cython
-        CIBW_SKIP: cp27-* cp34-* cp35-* pp*
+        CIBW_SKIP: cp27-* cp34-* cp35-* cp36-* pp*
         TWINE_USERNAME: qiskit
         CIBW_TEST_COMMAND: python {project}/examples/python/stochastic_swap.py
       steps:
@@ -96,7 +96,7 @@ stages:
       variables:
         python.version: '3.7'
         CIBW_BEFORE_BUILD: pip install -U Cython
-        CIBW_SKIP: cp27-* cp34-* cp35-* pp*
+        CIBW_SKIP: cp27-* cp34-* cp35-* cp36-* pp*
         CIBW_ARCHS_MACOS: universal2
         TWINE_USERNAME: qiskit
         CIBW_TEST_COMMAND: python {project}/examples/python/stochastic_swap.py
@@ -120,12 +120,10 @@ stages:
       condition: startsWith(variables['Build.SourceBranch'], 'refs/tags')
       variables:
         CIBW_BEFORE_BUILD: pip install -U Cython
-        CIBW_SKIP: cp27-* cp34-* cp35-* pp*
+        CIBW_SKIP: cp27-* cp34-* cp35-* cp36-* pp*
         TWINE_USERNAME: qiskit
         CIBW_TEST_COMMAND: python {project}\examples\python\stochastic_swap.py
       steps:
-        - {task: UsePythonVersion@0, inputs: {versionSpec: '3.6', architecture: x86}}
-        - {task: UsePythonVersion@0, inputs: {versionSpec: '3.6', architecture: x64}}
         - {task: UsePythonVersion@0, inputs: {versionSpec: '3.7', architecture: x86}}
         - {task: UsePythonVersion@0, inputs: {versionSpec: '3.7', architecture: x64}}
         - {task: UsePythonVersion@0, inputs: {versionSpec: '3.8', architecture: x86}}
@@ -506,8 +504,6 @@ stages:
       pool: {vmImage: 'windows-latest'}
       strategy:
         matrix:
-          Python36:
-            python.version: '3.6'
           Python38:
             python.version: '3.8'
           Python39:
@@ -587,8 +583,6 @@ stages:
       pool: {vmImage: 'ubuntu-latest'}
       strategy:
         matrix:
-          Python36:
-            python.version: '3.6'
           Python38:
             python.version: '3.8'
           Python39:
@@ -671,8 +665,6 @@ stages:
       pool: {vmImage: 'macOS-10.15'}
       strategy:
         matrix:
-          Python36:
-            python.version: '3.6'
           Python38:
             python.version: '3.8'
           Python39:
diff --git a/qiskit/__init__.py b/qiskit/__init__.py
index 990acd64af..24aa8d4ed8 100644
--- a/qiskit/__init__.py
+++ b/qiskit/__init__.py
@@ -58,14 +58,6 @@ from .version import QiskitVersion  # noqa
 __qiskit_version__ = QiskitVersion()
 
 
-if sys.version_info < (3, 7):
-    warnings.warn(
-        "Using Qiskit with Python 3.6 is deprecated as of qiskit-terra 0.17.0. "
-        "Support for running Qiskit with Python 3.6 will be removed in qiskit-terra 0.20.0.",
-        DeprecationWarning,
-    )
-
-
 class AerWrapper:
     """Lazy loading wrapper for Aer provider."""
 
diff --git a/releasenotes/notes/drop-python3.6-support-45ecc9e1832934cd.yaml b/releasenotes/notes/drop-python3.6-support-45ecc9e1832934cd.yaml
new file mode 100644
index 0000000000..f1465dce6b
--- /dev/null
+++ b/releasenotes/notes/drop-python3.6-support-45ecc9e1832934cd.yaml
@@ -0,0 +1,5 @@
+---
+upgrade:
+  - |
+    Support for running with Python 3.6 has been removed. To run Qiskit you need
+    a minimum Python version of 3.7.
diff --git a/requirements.txt b/requirements.txt
index 93068d4b86..835a0eeb40 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -10,7 +10,3 @@ python-dateutil>=2.8.0
 stevedore>=3.0.0
 symengine>=0.8 ; platform_machine == 'x86_64' or platform_machine == 'aarch64' or platform_machine == 'ppc64le' or platform_machine == 'amd64' or platform_machine == 'arm64'
 tweedledum>=1.1,<2.0
-
-# remove these once support for python 3.6 is dropped
-dataclasses>=0.8;python_version<'3.7'
-contextvars>=2.4;python_version<'3.7'
diff --git a/setup.py b/setup.py
index 23fc358870..abbc754108 100755
--- a/setup.py
+++ b/setup.py
@@ -112,7 +112,6 @@ setup(
         "Operating System :: MacOS",
         "Operating System :: POSIX :: Linux",
         "Programming Language :: Python :: 3 :: Only",
-        "Programming Language :: Python :: 3.6",
         "Programming Language :: Python :: 3.7",
         "Programming Language :: Python :: 3.8",
         "Programming Language :: Python :: 3.9",
@@ -123,7 +122,7 @@ setup(
     install_requires=REQUIREMENTS,
     setup_requires=["Cython>=0.27.1"],
     include_package_data=True,
-    python_requires=">=3.6",
+    python_requires=">=3.7",
     extras_require={
         "visualization": visualization_extras,
         "bip-mapper": bip_requirements,
diff --git a/tox.ini b/tox.ini
index 7f1cae1ca5..237640f057 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,6 +1,6 @@
 [tox]
 minversion = 2.1
-envlist = py36, py37, py38, lint-incr
+envlist = py37, py38, py39, lint-incr
 skipsdist = True
 
 [testenv]