Inter beat Bayern 2-0 in Madrid in May to become European champion for the first time since 1965, but neither side has so far replicated last season's good form.
Inter is seventh in the Italian league standings and only advanced as runner-up in the group stage, while Bayern topped a relatively weak group but is languishing in a distant sixth place in Germany.
Barcelona will meet Arsenal, which it beat in the 2006 final and outclassed 6-3 on aggregate in last season's quarterfinals, while Real Madrid is up against Lyon _ the side that knocked it out at the same stage last season.
Seven-time European champion AC Milan will play Tottenham, which won its group ahead of Inter in its first season in the Champions League.
Manchester United was drawn against Marseille, and Chelsea will meet FC Copenhagen. Shakhtar Donetsk, which won the second-tier UEFA Cup in 2009, is up against Roma, while Valencia plays Schalke.
The first leg matches are scheduled for Feb. 15.
The full draw:
AS Roma (ITA) v Shakhtar Donetsk (UKR)
AC Milan (ITA) v Tottenham (ENG)
Valencia (ESP) v FC Schalke (GER)
Inter Milan (ITA) v Bayern Munich (GER)
Lyon (FRA) v Real Madrid (ESP)
Arsenal (ENG) v Barcelona (ESP)
Marseille (FRA) v Manchester United (ENG)
Copenhagen (DEN) v Chelsea (ENG)
First legs will take place on February 15-16 and 22-23, second legs on March 8-9 and 15-16