Inter Milan face Barcelona, Tottenham Hotspur and PSV Eindhoven in Group B which features three former European champions.
Champions League runners-up Liverpool, Ligue 1 champions Paris St Germain and Serie A side Napoli were thrown together in the pick of the groups following the draw for this season's Champions League made on Thursday.
The trio were drawn into Group C alongside Red Star Belgrade, European Cup winners in 1991 and making their debut in the group stage.
Titleholders Real Madrid will face last season's semi-finalists AS Roma plus CSKA Moscow and Viktoria Plzen in Group G.
Juventus forward Cristiano Ronaldo will face his former club Manchester United after they were drawn together in Group H that also includes Spanish side Valencia.
Inter Milan, back in the competition for the first time since 2011/12, face Barcelona, Tottenham Hotspur and PSV Eindhoven in Group B which features three former European champions.
Champions League group stage draw:
Group A: Atletico Madrid, Borussia Dortmund, Monaco, Club Brugge.
Group B: Barcelona, Tottenham, PSV Eindhoven, Inter Milan.
Group C: Paris St-Germain, Napoli, Liverpool, Red Star Belgrade.
Group D: Lokomotiv Moscow, Porto, Schalke, Galatasaray.
Group E: Bayern Munich, Benfica, Ajax, AEK Athen.
Group F: Manchester City, Shakhtar Donetsk, Lyon, Hoffenheim.
Group G: Real Madrid, Roma, CSKA Moscow, Viktoria Plzen.