The Gunners will go head to head with the Italian side for a place in the group stage of the European competition.
The Premier League side were forced to compete in the play-off round after finishing fourth in the domestic league last season.
The draw, which was held in Switzerland, could have paired the London club with FC Twente, Odense, Rubin Kazan or FC Zurich.
The contest will be played over two legs on August 16/17 and August 23/24.
The full play-off round fixtures are as follows:
Wisla Krakow vs Apoel FC
Maccabi Haifa vs Genk
Dinamo Zagreb vs Malmo
FC Copenhagen vs Viktoria Plzen
BATE Borisov vs Sturm Graz
Odense vs Villarreal
FC Twente vs Benfica
Arsenal vs Udinese
Bayern Munich vs FC Zurich
Lyon vs Rubin Kazan