The two sides met at the same stage of last season's competition, Bayern triumphing on away goals after a 3-3 aggregate score.
Bayern went on to beat Borussia Dortmund 2-1 in May's final, part of an unprecedented treble in German football under the stewardship of Jupp Heynckes, with the Bundesliga and DFB-Pokal titles completing their impressive trophy haul.
Arsenal have progressed from the initial group stage for the 14th straight year, and - despite being ousted by Bayern at this stage last season - will take heart from a 2-0 victory at the Allianz Arena in the second leg of last season's tie.
Manchester City's reward for a first appearance in the knockout stages is a difficult encounter against Spanish champions Barcelona.
Gerardo Martino's men are looking to win the tournament for the first time since 2011 when they defeated Manchester United 3-1 at Wembley.
Last season's beaten finalists Dortmund face Zenit St Petersburg, while Real Madrid have been paired with Schalke.
Didier Drogba will make an emotional return to Chelsea after Galatasaray were drawn against his former employers.
The 35-year-old - who enjoyed an eight-year spell at Stamford Bridge - scored the winning spot-kick in Chelsea's 4-3 penalty shootout triumph over Bayern in the 2012 final.
David Moyes' Manchester United face Greek opposition in the form of Olympiacos, and Ligue 1 champions Paris Saint-Germain will meet Bayer Leverkusen in the first competitive meeting between the two sides.
In the other last-16 tie, La Liga high-flyers Atletico Madrid square off against Serie A giants Milan, who last lifted the trophy in 2008.
The first legs will be played in February, on the 18th, 19th, 25th and 26th, with the respective returns taking place three weeks later.
Draw in full: Manchester City v Barcelona, Olympiacos v Manchester United, Milan v Atletico Madrid, Bayer Leverkusen v Paris Saint-Germain, Galatasaray v Chelsea, Schalke v Real Madrid, Zenit St Petersburg v Borussia Dortmund, Arsenal v Bayern Munich.
