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.
Ticket details to be confirmed in due course.
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.
"We are doing well in the league but is the same as always, you have to be right, in the Champions League there is no time for mistakes, everything has to work, you have to be almost perfect in both games. We know the power and the strength of Liverpool - in the league they beat us, we beat them at home."
So, what do we know about our Premier League rivals?
City’s record against the Merseysiders is somewhat mixed over recent years with a 5-0 home win last September and our 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 will be a titanic north-west battle and probably one neither set of supporters really wanted at this stage!
Full Champions League quarter-final draw:
Barcelona v Roma
Sevilla v Bayern Munich
Juventus v Real Madrid
Liverpool v Man City
The teams have never met in European competition and the Reds’ Champions League past is unparalleled in England with five triumphs so far, the last of which came in 2005.
Here is a European fact-file on the Reds:
Jurgen Klopp – replaced Brendan Rodgers in October 2015 having previously managed Borussia Dortmund with whom he took to the UCL final in 2012/13 losing 2-1 to Bayern
2016/17 league position – 4th
2016/17 Champions League – Did not qualify for Champions League participation last season
Previous meetings – Never met in European competition (Premier League 17/18 City 5-0 Liverpool and Liverpool 4-3 City)
European Cup/ Champions League history – Five times champions (1976–77, 1977–78, 1980–81, 1983–84, 2004–05)
City links –James Milner, Raheem Sterling
UCL Group stage:
Liverpool won three and drew three of their six group matches, topping the table comfortably ahead of Sevilla. Spartak Moscow and Maribor were eliminated with the Reds scoring 23 goals and conceding six.
Round of 16:
Porto 0-5 Liverpool
Liverpool 0-0 Porto (agg 5-0)
Current Premier League position: 4th Premier League
Top scorer: Mo Salah 32