I have been working on this error for a long time now. I have Python 3.6 and Python 2.7. I have tried to install opencv 2 and 3 in Python 2.7 and Python 3.6 respectively. I
Faced with the same issue on Windows 10 I downloaded the open cv binary from the Unofficial Windows Binaries for Python Extension Packages.
Search the page for opencv and for and download the correct .whl for your system. Then pip install it. By example, on my system, after opening a cmd window I typed the following.
pip install opencv_python-3.4.1-cp36-cp36m-win_amd64.whl
I then opened python and the following worked
import cv2
print(cv2.__version__)
More info is available in this Mark Jay video.
:D
In Windows 10 you can install it as
pip install opencv-python
this will allow you to import cv2 module