The Gunners beat Bayern 2-0 in Munich at the same stage last season but went out on away goals - the German side having won 3-1 at the Emirates.
Arsenal now have Germany playmaker Mesut Ozil in their ranks, and Boateng admitted: "They're the toughest opponents we could have had. They'll be totally up for it after what happened last year. Both matches will be very intense."
City boss Manuel Pellegrini insists Barca are not the force they were two years ago despite adding Neymar to their star-studded squad.
"I think it is a beautiful game with two very good teams," Pellegrini said. "But Barcelona is not the team it was two years ago, so we will see how they arrive in February.
"I don't know exactly what happened inside Barcelona, but they changed three managers in the last three years and maybe the performance of the players is not the same."
The other two English sides had, on the face of it, easier draws for the first knockout round with Joe Mourinho's Chelsea facing their former striker Didier Drogba's Galatasaray, while David Moyes' Manchester United take on Greek champions Olympiacos.
Drogba said he was relishing his match against Chelsea, having scored the equaliser and then the winning penalty against Bayern Munich to win the competition in 2012.
"What a draw... I'm the luckiest man in this competition," he said on his official Instagram account. "In both games I'll be playing home! See you in few months."
In other matches, Real Madrid face German opposition in the form of Schalke, last year's runners up Borussia Dortmund take on Zenit St Petersburg, AC Milan will play in-form Spanish side Atletico Madrid while Bayer Leverkusen face big-spending Paris St-Germain.
- Sports & Recreation
- Bayern Munich
- Manuel Pellegrini
- Mesut Ozil