Arsenal have been drawn against current holders Bayern Munich.
Chelsea, the 2012 winners, face Galatasaray and Manchester United will meet Greek side Olympiakos.
Elsewhere, AC Milan face Atletico Madrid, Bayer Leverkusen meet Paris St-Germain, Schalke face Real Madrid and Zenit St Petersburg will meet last year’s runners-up Borussia Dortmund.
Chelsea and Manchester United have the advantage of playing the second leg at home after winning their groups, while City and Arsenal will have to travel away for the second legs of their ties.
City beat Bayern Munich 3-2 in their final Group D game and could have topped their group had they won 4-2.
City’s chief executive officer Ferran Soriano and director of football Txiki Begiristain used to work at Barcelona, who sold Yaya Toure to City in 2010.
Begiristain told his club’s official website: “I think it will be a great match. Ours is a team with a lot of confidence especially after winning against the champions in Munich – that will give us a lot of confidence.
“Our manager knows perfectly Barcelona because he managed in Spain for a long time. In this sense, we are confident.
“If you want to win the Champions League you have to beat the biggest teams, Barcelona are one of the biggest teams.”
City boss Manuel Pellegrini added: “I think Barcelona will be very concerned that they have drawn us. They are not the team of two years ago.”
Arsenal won 2-0 at Bayern Munich in March but went out on away goals in last season’s quarter-finals following a 3-1 defeat in the first leg, with the Germans going on to beat Dortmund in the final.
Bayern have also knocked the Gunners out of the tournament on their two previous meetings.
Chelsea will face Didier Drogba for the first time since the Ivorian striker left Stamford Bridge after eight years in 2012.
Blues manager Jose Mourinho claimed last week that a meeting with Drogba and Galatasaray was the draw he wanted.
Manchester United, who finished top of their group, have won each of their four previous meetings with Olympiakos.
Champions League round of 16 draw:
Manchester City v Barcelona
Olympiakos v Manchester United
AC Milan v Atletico Madrid
Bayer Leverkusen v Paris St-Germain
Galatasaray v Chelsea
Schalke v Real Madrid
Zenit St Petersburg v Dortmund
Arsenal v Bayern Munich
BBC SPORT
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