The Swedish side, who have been champions of their domestic league for the past two years, beat Red Bull Salzburg 3-2 on aggregate in the last round, having lost the first leg in Austria 2-0.
They currently sit mid-table in the Swedish league with eight wins and seven draws from 18 games so far and can number former Celtic player Jo Inge Berget in their ranks.
Malmo, beaten finalists in 1979, 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.
Manager Ronny Deila said that Celtic would not meet any team stronger than Qarabag – their opponents in the last round – in the play-off rounds.
However, assistant boss John Collins was keen to stress that Celtic supporters should not read too much into their Swedish opponent’s indifferent league form.
He said: “I know that they beat Salzburg by scoring three goals, that they are the Swedish champions and that they have not had a great start in their league.
“But I don’t think that is a real advantage. What you often find at this stage is that teams focus on Champions League qualification because you can catch up in the league later on so at this stage you tend to focus on these knockout games.
“I think all the teams that we could have played were all very good teams and having just come back from a long journey (to Azerbaijan) but you would also prefer a shorter journey.
“There’s always pressure and expectations but we all want to get into the Champions League group stages. That’s where everyone wants to be.”
The first leg will be played at Celtic Park on Wednesday, August 19 with the return at the Swedbank Stadion on Tuesday, August 25.
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)
Celtic (Sco) v Malmo (Swe)
Basel (Sui) v Maccabi Tel-Aviv (Isr)
BATE Borisov (Blr) v Partizan Belgrade (Srb)
Lazio (Ita) v Bayer Leverkusen (Ger)
Manchester United (Eng) v Club Brugge (Bel)
Sporting Lisbon (Por) v CSKA Moscow (Rus)
Rapid Vienna (Aut) v Shakhtar Donetsk (Ukr)
Valencia (Esp) v Monaco (Fra)