They are competing in Allsvenskan, the 2019–20 Svenska Cupen where they finished as runners-up, the 2020–21 Svenska Cupen, the 2019–20 UEFA Europa League where they were knocked out in the round of 32, and the 2020–21 UEFA Europa League where they were knocked out in the play-off round.

Malmö FF managed to play the round of 32 of the 2019–20 UEFA Europa League against VfL Wolfsburg and the group stage of the 2019–20 Svenska Cupen before the pandemic broke out.

Jon Dahl Tomasson replaced Uwe Rösler as the club's head coach after the latter's departure at the end of last season.

Anders Christiansen was appointed new club captain after Markus Rosenberg's retirement.

Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.