Cavani opened the scoring for the French champions after 42 minutes on Saturday by converting from the spot at Parc des Princes.
But it was his last contribution in the Ligue 1 clash, as he limped off during the final minutes of the first half.
PSG declined to make an immediate substitution, with Kylian Mbappe eventually replacing Cavani at the break.
First indications suggested that the forward felt discomfort in his right thigh, and post-match Thomas Tuchel confirmed a muscle injury, though the severity is something that is unknown at the current time.
"No, I don't have good news for you," Tuchel told Canal +. "It's not the big muscle, but a muscle is affected anyway. We must wait. I didn't see him or talk to the doctor.
"Honestly, I don't know if he will be here on Tuesday. If he leaves us at half-time, I'm afraid it's serious. The sight of the injury worries me. It is definitely not a good sign."
If Cavani does miss out only Mbappe will be available of the Ligue 1 leaders' famed attacking trident.
Neymar is also absent for PSG, having suffered a broken metatarsal against Strasbourg in January.
Between them, the trio have smashed an incredible 48 goals in the French top flight this season, as the Parisians have opened up a 13-point lead at the Ligue 1 summit.
And Tuchel conceded the loss of Cavani, combined with the absence of Neymar, would force him to reevaluate his entire gameplan for their biggest match of the season to date – the first leg of their Champions League tie with Manchester United.
"We have to rethink everything for Manchester United when players like that get hurt. We must wait for the results. We have already lost Ney," Tuchel added.
"It's too much. These are quality players and the game is decisive. We do not have a second Edi, nor a second Neymar.
"But we're ready for Manchester and I have faith in my players."
With Cavani now a doubt for Tuesday's clash at Old Trafford, a tie that looked rather favourable to PSG at the time of the draw now promises to be extremely challenging, with United in fine form since Ole Gunnar Solskjaer replaced Jose Mourinho on the United bench.
The Red Devils are unbeaten since December and pushed themselves into fourth place in the Premier League on Saturday with a convincing 3-0 defeat of Fulham, a position that looked near-impossible back in the dark days of Mourinho's final weeks in charge.