The Gunners, who qualified after completing a comprehensive play-off win over Fenerbahce this week, were placed in the tough-looking Group F at UEFA's draw in Monaco.
Celtic, who famously beat Barcelona last season, will face the Catalan giants again along with two other former winners in Group H in AC Milan and Ajax.
Manager Neil Lennon told Sky Sports News: "I think it is the best and the worst draw we could have got.
"In terms of glamour I don't think it comes any better than Barcelona, Ajax and AC Milan.
"In terms of football it is probably the most difficult group we could have got.
"But I think the hard work was really done last night and we can go and enjoy the tournament now."
Manchester City will again play reigning champions Bayern Munich - who they faced two years ago - CSKA Moscow and Viktoria Plzen in Group D.
Chelsea face two of the sides they conquered en route to last year's Europa League success in Basel and Steaua Bucharest, as well as Schalke, in Group E.
David Moyes' Champions League bow with Manchester United will come against Shakhtar Donetsk, Bayer Leverkusen and Real Sociedad in Group A.
Real Madrid have been drawn in the same group as Italian champions Juventus as they begin their latest hunt for an elusive 10th European Cup crown having last tasted success back in 2002.
Galatasaray and FC Copenhagen are the other sides in Group B.
Group G consists of three clubs who have lifted the UEFA Cup/Europa League in recent years with Atletico Madrid (2010 and 2012 winners), Porto (2011) and Zenit St Petersburg (2008) drawn together along with Austria Vienna.
French Ligue 1 champions Paris St Germain are in Group C with Benfica, Olympiacos and Anderlecht.
Champions League group-stage draw:
Zenit St Petersburg
Matchday one - September 17-18
Matchday two - October 1-2
Matchday three - October 22-23
Matchday four - November 5-6
Matchday five - November 26-27
Matchday six - December 10-11