Mbappe was left out of the PSG squad for Thursday's (AEDT) Champions League meeting with RB Leipzig at the Red Bull Arena due to "muscle discomfort" sustained in last weekend's 3-0 win over Nantes in Ligue 1.
The World Cup winner is set to be reassessed ahead of Sunday's meeting with Rennes, which comes before the international break.
Since his first away start in the Champions League in February 2017, Mbappe has been involved in 22 away goals (14 scored, eight assisted) in the competition – more than any other player.
Asked if there is a chance he could be without such an influential figure for longer than expected, Tuchel said: "It will not be longer. The injury is very minor.
"Unfortunately, he is in a risk zone. The doctor explained this to me. He couldn't be with the team. It's a shame for us. We can't take risks, that would have been too much. And we have to find solutions without Kylian."
Neymar, Mauro Icardi, Marco Verratti and Julian Draxler will all also be absent for the match in Germany, while Tuchel revealed Leandro Paredes is not fit enough to start.
With Angel Di Maria having only played twice in October due to a four-game ban in Ligue 1, the PSG boss was keen not to put too much pressure on the Argentine winger to play a leading role amid important absences.
"He's still a key player, but he also lacks rhythm. We shouldn't expect too much from him, he was suspended for four matches, he needs rhythm," said Tuchel.
"He likes to play a lot to gain confidence in dribbling and finishing. He only played the Champions League for us and I don't want to put all the pressure on him even though he's still a very important player."
PSG overcame Leipzig 3-0 in the semi-finals of the Champions League last season, with Di Maria scoring one and setting up Marquinhos and Juan Bernat for the others.
Tuchel acknowledged the back-to-back matches with the Bundesliga side will likely be pivotal in their hopes of reaching the knockouts, given they sit level with three points after two fixtures.
"We have the impression that it is like that in view of the first two matchdays," Tuchel said when asked if the games could be decisive in their campaign.
"It's a little bit like a round-of-16 tie I would say. We will play in Leipzig, then we will host Leipzig. This can be decisive, if we win the direct confrontation. We know the situation very well."
PSG is unbeaten in its past six away matches in the group stage and takes on Leipzig after Julian Nagelsmann's side suffered its heaviest European defeat, going down 5-0 to Manchester United last week.