I experienced the same issue. Resolved it by running Android studio with sudo from the command line:
sudo /Applications/Android Studio.app/Contents/MacOS/studio
After the update has been downloaded you have to run the command one more time for Android studio to copy over the correct files.
Next time you run Android studio with your non-privileged user it should be updated.
This also happened to me, but it was because the app was not in the
/Applications folder, after moving it to the right folder it ran without problems.
Case Android Studio is already under the Application folder run the following command on the terminal.
sudo chmod -R 777 /Applications/Android Studio.app/Contents