Nyon - Monaco, Champions League quarter-finalists last season, have been paired with Young Boys in the third qualifying round of this season's tournament.
Shakhtar Donetsk also must travel in the first leg to face Fenerbahce, who return to UEFA competitions after a two-year ban for match-fixing.
Ajax are away first against Rapid Vienna, and CSKA Moscow host Sparta Prague.
Panathinaikos were drawn at home to Bruges, though could yet go directly to the group stage as Greek champions Olympiakos are implicated in an ongoing criminal match-fixing investigation and could be expelled.
In a separate draw for national champions, Basel, who reached the last 16 last season, are away first against Lech Poznan or Sarajevo.
First-leg matches will be played July 28-29. Return matches are August 4-5.
Winners advance to the playoff round.
Champions League third qualifying round draw:
FK Sarajevo (BIH) or Lech Poznan (POL) v FC Basel (SUI)
Ludogorets Razgrad (BUL) or Milsami (MDA) v Sknderbeu (ALB) or Crusaders (NIR)
Ventspils (LAT) or HJK Helsinki (FIN) v Maribor (SLO) or Astana (KAZ)
Celtic (SCO) or Stjarnan (ISL) v Qarabag (AZE) or Rudar Pljevlja (MNE)
Trencin (SVK) or Steaua Bucharest (ROU) v Partizan Belgrade (SRB) or Dila Gori (GEO)
Midtjylland (DEN) or Lincoln (GIB) v APOEL Nicosie (CYP) or Vardar (MKD)
Hibernians (MLT) or Maccabi Tel-Aviv (ISR) v Viktoria Plzen (CZE)
Dinamo Zagreb (CRO) or Fola Esch (LUX) v Molde (NOR) or Pyunik (ARM)
The New Saints (WAL) or Videoton (HUN) v BATE Borisov (BLR) or Dundalk (IRL)
FC Salzburg (AUT) v Malmo (SWE) or Zalgiris Vilnius (LTU)
Panathinakos (GRE) v FC Bruges (BEL)
Young Boys Berne (SUI) v Monaco (FRA)
CSKA Moscow (RUS) v Sparta Prague (CZE)
Rapid Vienna (AUT) v Ajax (NED)
Fenerbahce (TUR) v Shakhtar Donetsk (UKR)
First legs - July 28/29
Second legs - August 4/5