Malmo defeated Rangers 2-1 in the third qualifying stage of this competition four years ago and humbled Hibs 9-0 – including a 7-0 rout at Easter Road – in Europa League qualifying in 2013.
The winners will progress to the Champions League group stages with the losers dropping into the same phase of the Europa League.
Full draw for Champions League play-offs:
Astana (Kaz) v APOEL (Cyp)
Skenderbeu (Alb) v Dinamo Zagreb (Cro)
Basel (Sui) v Maccabi Tel-Aviv (Isr)
BATE Borisov (Blr) v Partizan Belgrade (Srb)
Lazio (Ita) v Bayer Leverkusen (Ger)
Manchester United v Club Brugge (Bel)
Sporting CP (Por) v CSKA Moscow (Rus)
Rapid Vienna (Aust) v Shakhtar Donetsk (Ukr)
Valencia (Esp) v Monaco (Fra)