The content of the app, in the Pashto language, included official statements and videos from the Afghan movement.
The hardline group blamed “technical issues” for its disappearance shortly after it launched on 1 April.
However the BBC understands it was taken down because it violated a Google app policy which prohibits hate speech.
It was discovered and reported by a US-based organisation called Site Intel Group which monitors jihadist activity.
Google declined to comment on specific app issues.
“Our policies are designed to provide a great experience for users and developers. That’s why we remove apps from Google Play that violate those policies,” it said in a statement.
A spokesman from the Taliban told Bloomberg the app was “part of our advanced technological efforts to make a more global audience”.