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The Round of 16 ties will be over two legs with the matches split over two weeks.
Man 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 at the Etihad Stadium on Tuesday February 21 (TBC) with the second leg played on March 15 (TBC) at the Stade Louis II.
"Monaco are playing the best football in France right now - this will be a very difficult game for us," said Man City's Director of Football Txiki Begiristain. Get his full reaction on mancity.com.
"We are just happy to be here and we are looking forward to this tie."
Man City have never met Monaco in a competitive game before. The Ligue 1 side are currently one point behind leaders Nice and beat Bordeaux 4-0 away last weekend as they chase their first title since 1999/2000.