Uruguay striker Cavani found the back of the net with a 42nd-minute penalty but he was soon hobbling off the pitch while clutching his thigh, three days before PSG travel to Old Trafford for their last-16, first leg Champions League tie.
“I don’t have good news. We have to wait,” said coach Thomas Tuchel.
Tuchel's side will also be without Brazil striker Neymar, who has been ruled out with a foot injury.
"I honestly don’t know if Cavani will play. Yes it is worrying. We don’t have another Edi like we don’t have another Neymar."
The result put leaders PSG on 59 points from 22 games, 13 ahead of second-placed Lille, who have played one more game.
The was some good news for PSG as midfielder Marco Verratti returned to the line-up after recovering from an ankle injury.
Verratti played almost an hour before being substituted by Leandro Paredes.
The Italian is now expected to start on Tuesday against a resurgent United side who claimed their 10th win in 11 games under caretaker coach Ole Gunnar Solskjaer when they beat Fulham 3-0 on Saturday.
PSG, who suffered their first league defeat this season against Olympique Lyonnais last weekend, were in control against mid-table Bordeaux.
Cavani broke the deadlock with a penalty for his 17th goal in 16 league games this season after Thomas Meunier had been fouled in the area. Meunier was later replaced following a head clash with a Bordeaux player.
A couple of minutes later Cavani limped off the pitch, prompting Tuchel to substitute him with Kylian Mbappe, who had been expected to be rested ahead of Tuesday's clash.
The French international is now likely to start as a lone striker at Old Trafford, supported by Julian Draxler and Angel Di Maria.
The second half was relatively poor, with PSG players, wearing shirts with their names written in Mandarin to mark the Chinese New Year, taking no risks and a Bordeaux side lacking in creativity.
The visitors' only clear chance after the break came in the 61st minute when Gianluigi Buffon pulled off a superb save to tip away Francois Kamano's 25-metre strike.
Bordeaux are 12th on 28 points.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
