A pending match-fixing case involving Fenerbahce at sport's highest court means the Turkish club could be expelled from the competition even if it wins. The first leg is scheduled Aug. 21 in Istanbul.
"We put the politics aside and Arsenal will concentrate on the football side," Arsenal official David Miles told The Associated Press after the draw. "We will keep in touch with UEFA."
Seven-time winner AC Milan was paired in the draw with PSV Eindhoven, the 1988 European champion, with the first match in the Netherlands.
"It's a classic European cup match-up," Milan director Umberto Gandini said. "It's a pleasure to play with such a historical club, and it's a difficult task."
Schalke was drawn to play Metalist Kharkiv, which is also threatened with UEFA sanctions for a years-old domestic match-fixing case. The Ukrainian club faces a disciplinary hearing at UEFA on Tuesday.
Among the 10 pairings it was: Lyon vs. Real Sociedad, Portuguese newcomer Pacos de Ferreira vs. Zenit St. Petersburg and Shakhter Karagandy hosting Celtic. The Scottish champion faces a long trek to Kazakhstan for the first match, at the national stadium in Astana.
First legs are played Aug. 20 or 21 and return matches on Aug. 27 or 28.
Winners advance to the elite 32-team group stage, joining established powers like defending champion Bayern Munich, Barcelona, Real Madrid and Manchester United. It will be drawn Aug. 29 in Monaco.
The Court of Arbitration for Sport has set an Aug. 28 deadline — the day after Arsenal hosts the return leg — to rule on Fenerbahce's appeal against a two-year ban from UEFA competitions. No hearing date has been set.
UEFA's Champions League rules require clubs not to have been involved in fixing matches since April 2007, and several Fenerbahce officials were convicted in a criminal trial of fixing matches during the club's 2011 national title run. They deny wrongdoing.
Metalist also faces UEFA sanctions after CAS last month dismissed an appeal by the Ukrainian club's sports director against a five-year ban from football. The Ukrainian federation had judged that Metalist's 4-0 win against Karpaty Lviv in an April 2008 league match was fixed.
Metalist vice-president Konstantin Pivovarov confirmed that, even if UEFA rules against the club, it is likely to appeal that verdict at CAS and try to continue in the competition.
"We're expecting to play Metalist," Schalke official Moritz Beckers-Schwarz said.
If Metalist is removed, its defeated third qualifying round opponent — PAOK Thessaloniki, led by a former Schalke coach — could in theory be reinstated.
"We would like to play PAOK because Huub Stevens is the coach now and that would be an interesting issue," Beckers-Schwarz said.
Fenerbahce eliminated Salzburg this week in the qualifying round.
Two years ago, the Fenerbahce case led to its withdrawal from the groups draw by the Turkish football federation on the eve of the Monaco event. Trabzonspor was restored in its place despite previously losing in the qualifiers.
Other pairings Friday were: 1986 champion Steaua Bucharest vs. Legia Warsaw, Viktoria Plzen vs. Maribor, Dinamo Zagreb vs. Austria Vienna, Ludogorets Razgrad vs. Basel.