The Turkish side are awaiting a final ruling over whether they will be allowed to go into the competition proper this season, having been banned from competing in Europe by UEFA for match-fixing in domestic competition.
They have challenged that ruling and a CAS verdict is due before the group stage draw is made, but home and away matches against Arsenal stand to go ahead before that decision arrives.
UEFA said no decision has yet been made regarding what would happen in the event of Fenerbahce winning the tie and losing their CAS appeal.
Fenerbahce finished second in the Turkish Super Lig last season, while Arsenal took fourth place in the Premier League.
Scottish champions Celtic face a long journey to Asia after they were drawn against the Kazakhstan champions Shakhter Karagandy.
Celtic came through 1-0 on aggregate against Elfsborg in the third qualifying round, winning at Parkhead and then holding on for a hard-earned goalless draw in Sweden on Wednesday night.
Neil Lennon's team made it through to the last 16 last season, beating Barcelona at home in the group stages to advance along with the Spanish giants before bowing out to Juventus.
It proved a lucrative run for the Glasgow club, who will now face a team who have no European pedigree, aiming to reach a main-draw stage for the first time. Celtic, by contrast, won the old European Cup in 1967.
Shakhter landed the Kazakh league title in 2012, but their form in 2013 has been shaky. They ended the regular season in third place, behind Aktobe and Astana, and are heading into the championship round of the domestic campaign.
French side Olympique Lyonnais were also given a tricky tie against Spain's Real Sociedad.
The first-leg of the play-offs will be played on the 20th & 21st of August with the second-leg being played on the 27th.
Dinamo Zagreb v FK Austria Vienna
Ludogorets v Basle
Viktoria Plzen v Maribor
Shakhter Karagandy v Celtic
Steaua Bucharest v Legia Warsaw
Lyon v Real Sociedad
Schalke 04 v FC Metalist Kharkiv
Pacos Ferreira v Zenit St Petersburg
PSV v AC Milan
Fenerbahce v Arsenal