Zenit to face AEL Limassol in Champions League
Zenit made the round of 16 last season before bowing out to Borussia Dortmund 5-4 on aggregate, while Cypriot side AEL reached the group stage in 2012-13.
Copenhagen finished bottom of Group B last term and will face Dnipro Dnipropetrovsk while Red Bull Salzburg - who made the final 16 of the Europa League - will face Valletta or Qarabag.
Feyenoord's first European test of the post-Ronald Koeman era will see them take on Turkish Super Lig club Besiktas.
Scottish champions Celtic could face a relatively nearby fixture provided they can see off KR at Celtic Park.
Ronny Deila's men secured a one-goal advantage in Reykjavik and will meet Legia Warsaw or Dublin-based St Patrick's Athletic in the next round if they see the tie through.
Lille's reward for a third-place finish in the French top flight last term is a fixture with Grasshoppers of Switzerland while Standard Liege will welcome Panathinaikos of Greece for the first leg of their tie.
If Maccabi Tel-Aviv get past Santa Coloma they will likely lose home advantage for their tie with Zrinjski or Maribor.
UEFA ruled on Thursday that, due to the "current security situation in Israel", no UEFA competition matches would be played in the country until further notice.
Draw in full (Champions Route):
Limassol v Zenit
Dnipro Dnipropetrovsk v Copenhagen
Feyenoord v Besiktas
Grasshoppers v Lille
Standard Liege v Panathanaikos
Valletta or Qarabag v Red Bull Salzburg
Cliftonville or Debrecen v BATE Borisov or KC Skenderbeu
Slovan Bratislava or The New Saints v Sheriff or Sutjeska
Aalborg v Dinamo Zagreb or Zalgiris
Legia Warsaw or St Patrick's Athletic v KR or Celtic
Dinamo Tbilisi or Aktobe v Stromsgodset or Steaua Bucharest
Zrinjski or Maribor v Santa Coloma or Maccabi Tel-Aviv
Rabotnicki or HJK Helsinki v APOEL
Sparta Prague or Levadia Tallin v Malmo or Ventspils
Ludogorets or F91 Dudelange v Partizan or HB Torshavn