diff --git a/setup.py b/setup.py
index e892126c63..f20e5d67ff 100644
--- a/setup.py
+++ b/setup.py
@@ -31,7 +31,8 @@
     'qiskit-terra>=0.12.0',
     'numpy>=1.16.3;python_version>"3.5"',
     'numpy>=1.16.3,<1.19.0;python_version<"3.6"',
-    'scipy>=1.0',
+    'scipy>=1.0;python_version>"3.5"',
+    'scipy>=1.0,<1.5.0;python_version<"3.6"',
     'cython>=0.27.1',
     'pybind11>=2.4'  # This isn't really an install requirement,
                      # Pybind11 is required to be pre-installed for