Fenerbahce were given a two-year ban from European competition in June over match-fixing allegations but were later reinstated while an appeal is heard.
The Gunners will face the Turkish runners-up away on 21 August, with the home leg six days later.
Celtic travel to Kazakhstan champions Shakhter Karagandy for their first leg.
Tottenham have been drawn away to Georgian outfit Dinamo Tbilisi in the first leg of the Europa League play-off tie for a place in the main draw.
