Jose Mourinho’s side Tottenham will also be on the road in the first leg to tackle Dinamo Zagreb.
Scottish Premiership leaders Rangers drew Slavia Prague. Their first will be an away for Rangers.
The draw was made on Friday afternoon in Nyon, Switzerland at the House of European Football.
There were no seedings in the draw.
Arsenal and Olympiacos met at the Round of 32 last year.
In the first leg on 20 February, Arsenal defeated the Turkish side 1-0 at home.
But Olympiacos beat Arsenal in the second leg at the Emirates 2-1, thus qualifying on aggregate goals.
The ties will be played over 11 and 18 March.
Draws for the quarter and semi-finals will then be held on 19 March.
The full draw
Ajax vs Young Boys
Dynamo Kiev vs Villarreal
Roma vs Shakhtar Donetsk
Olympiacos vs Arsenal
Dinamo Zagreb vs Tottenham Hotspur
Man Utd vs AC Milan
Slavia Prague vs Rangers
Granada vs Molde
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