The Red Devils have qualified for Europe's premier competition for the first time in their five-year history after finishing second in the Women's Super League last season.
And French giants PSG stand in their way of group stage qualification.
United will host the first leg of the play-off tie on October 10 or 11, with the second leg tie to take place the following week.
If United win, they will join holders Barcelona, WSL champions Chelsea as well as Lyon and Bayern Munich in the main draw.
Though Arsenal will not be involved in the Champions League, after last season's semi-finalists were knocked out by Paris FC in the first qualifying round last weekend.
Elsewhere, Glasgow City will face Norwegian club SK Brann after they won the Scottish Women's Premier League last season.
It's been a tumultuous summer for United, having parted ways with a number of key players.
Lionesses legend Alessia Russo has joined Arsenal on a free transfer.
Meanwhile Spanish World Cup winner Ona Battle and Norwegian midfielder Vilde Boe Risa have linked up with Barcelona and Atletico Madrid respectively.
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But they have made up for it by signing another World Cup winner, Irene Guerrero, as well as World Cup Golden Boot winner Hinata Miyazawa.
Crucially, United have so far retained England's number one goalkeeper Mary Earps, despite interest from a number of clubs.
Despite a world-record bid being made for Earps by Arsenal, she will now remain at United until at least January.