The Red Devils duo have not travelled to Paris for Tuesday's European clash, which you can listen to LIVE on talkSPORT (kick-off 8pm).
Maguire suffered a knock on international duty last week.
He featured - and scored - in Saturday's defeat of Newcastle but will rest for this one, with one eye on Saturday's game vs Chelsea.
His absence means influential January arrival Bruno Fernandes will wear the armband instead.
Fernandes was surprised by Ole Gunnar Solskjaer in the pre-match press conference by being named as skipper while sitting alongside his manager.
Cavani, meanwhile, only started training with his new teammates on Sunday having been quarantining since signing for United on deadline day.
Not travelling to Paris means Cavani will not debut against his former club PSG, for whom he is the all-time leading goalscorer, and he will instead hope to make his debut against Chelsea.
Nonetheless, there will be some players facing their former clubs on Tuesday night.
Ex-Man United stars Angel Di Maria and Ander Herrera are in contention to start for the hosts - who are in the middle of a serious injury crisis.
And there could be a debut for the Red Devils after all, with Alex Telles in line to play for the first time since his deadline day arrival from Porto.
Besides Maguire and Cavani, Man United are again without Mason Greenwood, who missed the 4-1 victory over Newcastle, as well as Eric Bailly leaving the Red Devils short in defence.
There have been rumours of disciplinary issues surrounding Greenwood, but boss Ole Gunnar Solskjaer has insisted it is due to an unspecified injury problem.
Paul Pogba will hope to be recalled to the starting XI in his homeland, having been dropped at St James' Park following some indifferent form.
"We're a little bit depleted but we have got more than enough players," Solskjaer said at his press conference.
"We hope the players won't be away for too long. Edinson needs a few more days training before maybe we can think about the weekend. Hopefully Harry, Eric and Mason as well but we're not sure about that."
As for the hosts, PSG have a seriously long injury list too, which has seen manager Thomas Tuchel claim he might only have 11 fit players available.
Mauro Icardi, Juan Bernat and Thilo Kehrer will all sit out due to injury, while Marquinhos, Marco Verratti, Julian Draxler and Danilo Pereira are major doubts after missing Friday's victory over Nimes.
Meanwhile, Leandro Paredes could be out after suffering an injury against their Ligue 1 rivals.
Neymar and Kylian Mbappe will both play as they look to continue their fruitful partnership which has yielded 166 goals over the past four seasons.
How PSG could line up
How Man United could line up
Listen to PSG vs Man United LIVE on talkSPORT at 8pm on Tuesday!
Harry Maguire and Edinson Cavani will not play in Manchester United's Champions League opener against PSG tonight.