A similar situation arises on Fedora 25, on which I was able to solve this. Your mileage may vary on Ubuntu.
First note that wxPython is available in two major versions, let's call them wx3 and wx4. You can identify your running version through import wx; print(wx.version()). The version string on Fedora 25 reads '3.0.2.0 gtk3 (classic)', i.e. a brand of wx3. On sourceforge these versions are known as 'wxPython' and 'wxPython4', and wxpython.org calls wx4 'phoenix'.
Inspecting the source code of wx3 you will note that wx3's syntax is incompatible with python3. Conversely, wx4 is compatible both with python2.7 and python3.
wx4 doesn't seem to be available on Fedora 25, therefore python3 can't run any wx out-of-the-box. Ubuntu may or may not have the same issue.
The following worked for me to install wx4 in a python3 virtual environment:
pip install -U -f https://extras.wxpython.org/wxPython4/extras/linux/gtk3/fedora-26 wxPython
I presume the answer to your question would be
pip install -U -f https://extras.wxpython.org/wxPython4/extras/linux/gtk3/ubuntu-16.04 wxPython
In case you need to port a (py2, wx3) application to python3, you would be wise creating an intermediate step: (py2, wx3) -> (py2, wx4) -> (py3, wx4), noting that (py3, wx3) is an impossibility.
To create the (py2, wx4) environment was more cumbersome for me, because the above pip install command fails to find header files when run using pip2.
What ended up working for me was to download the 4.0.0b2 source https://pypi.python.org/packages/bc/6f/f7bb525517557e1c596bf22ef3f242b87afaeab57c9ad460cb94b3b0714e/wxPython-4.0.0b2.tar.gz#md5=2e3716205da8f52d8039095d14534bf7
and follow the build instructions https://github.com/wxWidgets/Phoenix/blob/master/README.rst , from which I only used the build command python build.py dox etg --nodoc sip build .
After building, you need to tell your python2 where to find the wx4 library. I ended up doing that by creating a virtualenv, and creating a symbolic link like so:
/home/user/venv/lib/python2.7/site-packages/wx -> /home/user/downloads/wxPython/wxPython-4.0.0b2/wx
That latter directory cointaining the result of the build.