diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
index a6dfb13dd..3cad0f626 100644
--- a/.github/workflows/main.yml
+++ b/.github/workflows/main.yml
@@ -10,7 +10,7 @@ jobs:
     runs-on: ${{ matrix.os }}
     strategy:
       matrix:
-        python-version: [3.5, 3.6, 3.7, 3.8]
+        python-version: [3.6, 3.7, 3.8]
         os: ["macOS-latest", "ubuntu-latest"]
     steps:
       - uses: actions/checkout@v2
diff --git a/releasenotes/notes/drop-py35-1a7810120bfa3bef.yaml b/releasenotes/notes/drop-py35-1a7810120bfa3bef.yaml
new file mode 100644
index 000000000..16ff7feaf
--- /dev/null
+++ b/releasenotes/notes/drop-py35-1a7810120bfa3bef.yaml
@@ -0,0 +1,8 @@
+---
+upgrade:
+  - |
+    The deprecated support for running qiskit-ignis with Python 3.5 has
+    been removed. To use qiskit-ignis >=0.5.0 you will now need at
+    least Python 3.6. If you are using Python 3.5 the last version which will
+    work is qiskit-ignis 0.4.x.
+
diff --git a/setup.py b/setup.py
index fec7c9de5..a9db9a750 100644
--- a/setup.py
+++ b/setup.py
@@ -69,7 +69,6 @@
         "Operating System :: MacOS",
         "Operating System :: POSIX :: Linux",
         "Programming Language :: Python :: 3 :: Only",
-        "Programming Language :: Python :: 3.5",
         "Programming Language :: Python :: 3.6",
         "Programming Language :: Python :: 3.7",
         "Programming Language :: Python :: 3.8",
@@ -83,6 +82,6 @@
     },
     install_requires=requirements,
     include_package_data=True,
-    python_requires=">=3.5",
+    python_requires=">=3.6",
     zip_safe=False
 )
diff --git a/tox.ini b/tox.ini
index daf378e60..f3b9931d3 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,6 +1,6 @@
 [tox]
 minversion = 2.1
-envlist = py35, py36, py37, py38, lint
+envlist = py36, py37, py38, lint
 skipsdist = True
 
 [testenv]