Meanwhile, Atletico Madrid, who are the favourites to win the competition along with the Premier League outfit, have been paired with Sporting CP in the last eight. The other ties see RB Leipzig tackle Marseille and Lazio face Salzburg.
The Europa League now looks the Gunners' most realistic chance of reaching the Champions League next season, as they lie 12 points shy of fourth-placed Tottenham, though they face a Russian side that dumped out Lyon from the competition on away goals at the last-16 stage.
Arsenal beat Milan 5-1 on aggregate over two legs, winning 2-0 in Italy and 3-1 in north London.
CSKA lie third in the Russian league table, level on points with second-placed Spartak Moscow, and eight points behind leaders Lokomotiv.
Atletico thumped Lokomotiv over two legs, winning 8-1 on aggregate, while their quarter-final opponents, Sporting, beat FK Viktoria Plzen 3-2 on aggregate, despite a 2-1 second leg defeat.
These fixtures will be played on April 5 and 12.
The Europa League semi-final draw will take place on April 13, and the final will be played on May 16 at Groupama Stadium in France.