Mbappe played the full game as PSG lost 2-1 to the Premier League leaders in the first leg of the semi-final on Wednesday.
However, the France international – who did not have a shot against City, though he did create four chances – is not fit to feature against Lens in Ligue 1, denying him the chance to add to his tally of 25 goals in the competition this season.
PSG boss Mauricio Pochettino was vague in his response when asked about the chances of Mbappe returning in time to play at the Etihad Stadium on Tuesday.
"Kylian has a problem with his right calf," Pochettino told the media. "We hope it is not serious and that he can be back with us as soon as possible.
"He is an important player for us and when you don’t have a key player, it always has an impact. But we have players in the squad who can do well and fill in for him.
"This will get us close to the victory that we want, which is the most important thing."
PSG led 1-0 at half-time against City, captain Marquinhos heading them in front in the 15th minute at Parc des Princes. However, Pep Guardiola's side hit back impressively after the break, turning the game around thanks to goals from Kevin De Bruyne and Riyad Mahrez.
Despite the disappointing result, Pochettino insists the mood within the squad remains positive - and made clear the immediate focus is on the Ligue 1 title race, rather than the return meeting with City.
"After losing in the Champions League, the players want to be competing again to get over that bad feeling," Pochettino said.
"The players are doing well. We lost the first leg but are motivated and convinced that we can turn it around.
"With all respect to Manchester City, we will go there to play the game. The mood is good; we are motivated for the game tomorrow, which is the most important one."
Asked about the tactical approach for the second leg, he replied: "We want to reaffirm the positive things that we did in the first leg – and there were many of them. I think we have to analyze that.
"We did very well in the first half and were superior to City. We were in the second half as well, but after conceding two goals, which were tough blows for us to take, plus the sending off [of Idrissa Gueye], meant that we played with less players.
"The team remained mentally strong against a very good Manchester City team. In terms of tactics, we will be ready for a battle."