The date of the away and home legs will be confirmed in due course, but City will play the first leg Away in Switzerland.
The Blues have never met FC Basel competitively.
Manchester City Director of Football Txiki Begiristain said: "We have to respect FC Basel and we have to be careful.
"We need to be ready to play them and do our best because obviously we want to go as far as we can in this competition
"We showed against Napoli that we can do well home or away. We had to fight to qualify and to win the group and I think we've shown the character and personality needed to do well in the Champions League."