The Gunners are aiming to win the Europa League title for the first time and earn a spot at next season's Champions League, but will face a CSKA side brimming with confidence after knocking out Lyon this week.
Two-time Europa League winners Atletico will be facing Portuguese side Sporting Lisbon in their last-eight showdown. The Rojiblancos won the title in 2010 and 2012.
Elsewhere, German side RB Leipzig will take on French outfit Olympique de Marseille, while the Serie A's Lazio play host to the first Austrian side to make it as far as the quarter-finals, RB Salzburg.
The quarter-final first legs will be played on April 5, with the second legs played on April 12.
RB Leipzig v Olympique de Marseille
Arsenal v CSKA Moscow
Atletico Madrid v Sporting Lisbon
Lazio v RB Salzburg