The forward suffered a nasty-looking ankle injury in PSG's Coupe de France final victory over Saint Etienne, and was forced to depart after only 33 minutes last Friday.
PSG and Atalanta will lock horns in the last eight of the Champions League on August 12, and Tuchel is not optimistic about Mbappe's chances of recovering in time.
"This will have an important influence for us, but I hope that the solution will be found," Tuchel told reporters.
"We still hope [he can play against Atalanta], but the chances will be very, very small. Every day counts to achieve a miracle, but tomorrow we will have to adapt without Kylian."
Mbappe has been in prolific form for the Ligue 1 champions this season and has notched up 30 goals in 34 games across all competitions.