Brugge finished top of the Belgian league last season but were second in the title play-offs, while Malmo are sixth in the Swedish league.
The first legs of the play-off ties will take place on 18-19 August, with the second matches on 25-26 August.
Southampton face Danes FC Midtjylland in the Europa League play-off round.
Ronald Koeman’s side, who beat Vitesse Arnhem in the last round, are at home for the first leg on 20 August, before travelling to Denmark a week later.
The winners of the Champions League and Europa League play-off rounds will progress to the group stages of their respective competitions.