The Blues will travel to Anfield for the first leg on 4 April, with the return leg a week later at the Etihad Stadium on 10 April.
It is the first meeting between the two clubs in European competition.
Reacting to the draw in Switzerland, Director of Football Txiki Begiristain said: “It’s a very difficult one. We like to travel and to go to another country in the Champions League but it is what it is.
“We know each other very well, they are a very offensive team, the truth is it is going to be a great couple of games and we are going to see good football.
City’s record against the Merseysiders is somewhat mixed over recent years with a 5-0 home win last September and their only Premier League this campaign loss coming at Anfield in a 4-3 thriller last January.
The Blues’ record at Anfield,one victory in 37 years, may not daunt Pep Guardiola’s side, but it’s fair to say this would be a titanic north-west battle and probably one neither set of supporters really want at this stage.
In the other ties, Barcelona face Roma, Sevilla conquerors of Manchester United take on Bayern Munich and Juventus will play Real Madrid