The Round of 16 ties will be over two legs with the matches split over two weeks.
City, as an unseeded team, will play the first leg at home with the dates to be confirmed shortly.
The first leg will take place on Tuesday, February 21 with the second leg away in the Principality taking place on Wednesday, March 15.
“Monaco are playing the best football in France right now - this will be a very difficult game for us,” said City director of football Txiki Begiristain.
“We are just happy to be here and we are looking forward to this tie.”
The full draw...
CITY v AS Monaco
Sevilla v Leicester
Real Madrid v Napoli
Benfica v Borussia Dortmund
Bayern Munich v Arsenal
Porto v Juventus
Bayer Leverkusen v Atletico Madrid
PSG v Barcelona