They will have gone more than nine weeks without a competitive fixture by the time they face Celtic.
Celtic have been paired with Zenit St Petersburg in the Europa League knockout stages.
Arsenal face potentially tough tasks in Borussia Dortmund and Napoli, who are also unseeded teams who came third in their Champions League group.
Celtic were in the draw after finishing third in their Champions League group.
Brisk Monday ahead with snow chances on the rise tonight
Breezy northwesterly winds certainly added a chill to the air giving wind chills or feel-like temperatures in the 20's. Highs on Tuesday afternoon will be in the mid teens, and lows will be around 1° early Wednesday morning.
The first leg, to be played at Jamtkraft Arena, will take place on on Thursday, February 15 with the return match on Thursday, February 22.
Following a third-place finish last season, they are now fourth in Russia's Premier League.
Celtic midfielder Olivier Ntcham has claimed on Twitter that it is "never easy" to go to Russian Federation after being drawn against Zenit St. Petersburg in the Europa League.
Arsenal will consider their clash against Swedish upstarts Ostersunds as encouraging, having waltzed through at the top of their group with relative ease.
France is also well represented in the round of 32, with Nice and Marseille reaching the next phase alongside Lyon, with the former pair preparing to face respective opponents Lokomotiv Moscow and Braga.
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