Mbappe left the field in the second half to be replaced by Arthur Zagre as the Parisians returned to winning ways with a 4-0 victory.
PSG, who are already without Neymar, as the Brazilian continues to be linked with a move back to Spain, also lost striker Edinson Cavani and defender Abdou Diallo in the same match.
The French champions released a statement on Monday confirming Mbappe’s unavailability for the next four weeks.
"Kylian Mbappé injured his left hamstring yesterday," a statement on PSG's website read.
"This morning's tests confirm an absence of four weeks depending on the recovery."
The injury means Mbappe will miss PSG’s upcoming Ligue 1 games against Metz and Strasbourg, and his availability for their Champions League opener in the middle of September is also in huge doubt.
France manager Didier Deschamps will also not be able to call upon the services of the 20-year-old world cup winner for their Euro 2020 qualifying games against Albania and Andorra next week.
The prognosis of Cavani’s injury will also keep out the Uruguayan for three weeks.
"Cavani, who also injured during Sunday night's game at the right hip, had an MRI scan this morning," PSG's statement added.
"The recovery time will be refined in the coming days but is not expected before three weeks."
