I installed Python 3.6 on Ubuntu 16.04 by using Jonathon Fernyhough\'s PPA:
sudo add-apt-repository ppa:jonathonf/python-3.6
sudo apt-get update
sudo apt-get
I solved this issue for Python 3.6 by first installing the python-apt package for Python 3:
sudo apt install python3-apt
After that, I changed to the dist-packages directory and copied the apt_pkg[...].so file to the new default file name apt_pkg.so, to be also recognized by Python 3.6:
cd /usr/lib/python3/dist-packages
sudo cp apt_pkg.cpython-34m-i386-linux-gnu.so apt_pkg.so
Now all ModuleNotFoundError: No module named 'apt_pkg' exceptions disappeared on expectedly thrown error messages.