PSG will are already be missing superstar striker Neymar, sidelined until at least April with a foot injury, while Manchester United have won ten of their eleven games under new coach Ole Gunnar Solskjaer.
French sports daily L'Equipe reported earlier on Sunday that a medical had revealed a torn right-thigh muscle for Cavani, but PSG reported shortly afterwards the problem was the right hip.
"The tests carried out have shown an injury in the right hip. The treatment and the amount of recovery time will depend on how he reacts over the next few days," PSG said on their website.
L'Equipe suggested Cavani, known as El Matador for his clinical finishing, would also miss the return leg March 6.
Earlier Sunday Tuchel described Cavani's situation, stemming from a fiercely converted penalty on Saturday, as bleak.
"There is no good news for Edi this morning," he said.
"In my opinion the news is not going to be very good," Tuchel said.
"It will be very difficult for him to play," he predicted.
The Uruguayan centre-forward has scored 17 times in the French league and twice in the Champions League this season.
PSG visit Old Trafford on Tuesday for the first leg of their encounter in the round-of-16, the stage at which the French champions went out in the last two seasons.
Tuchel said there was good news for another of his key players, midfielder Marco Verratti who started against Bordeaux after three weeks out with an ankle problem.
"Verratti can play and will play," said the German coach.
"I'm worried because we are missing key players," said Tuchel. "For the big games in the Champions League, it is absolutely necessary to have key players with a lot of experience".