The Gunners made it into the draw despite losing at home to Swedish side Ostersund on Thursday night — progressing 4-2 on aggregate.
Now they come up against seven-time European Cup winners Milan, who saw off Ludogorets to reach this stage.
Both sides are struggling domestically; Arsenal are sixth in the Premier League while Milan languish seventh in Serie A but have not lost in all competitions since the turn of the year.
The first leg will take place at the San Siro as Gennaro Gattuso looks to mastermind victory over Arsene Wenger’s men.
Elsewhere, Borussia Dortmund will face Red Bull Salzburg and Aletico Madrid take on Lokomotiv Moscow.
Lazio meet Dynamo Kiev, RB Leipzig have been drawn against Celtic’s conquerors Zenit St Petersburg, CSKA Moscow face Lyon — who will be hosting this year’s final — while fellow Ligue 1 side Marseille tackle Athletic Bilbao and Sporting Lisbon play Viktoria Plzen.
All opening legs will take place on March 8, with the ties concluding on March 15.