Neymar was forced off inside half an hour in Instanbul with match still scoreless as PSG faced the Turkish side in the second match of the group stage
The winger was forced out after 26 minutes, having previously come off the pitch a few minutes earlier due to an apparent injury.
PSG are in the middle of a packed run of fixtures, with another three matches to come in the next 10 days prior to another international break.
They face Nantes in Ligue 1 on Saturday, with a trip to RB Leipzig and another league match against Rennes to come next week.
Neymar could be a doubt for Brazil's World Cup qualifiers against Venezuela and Uruguay next month, depending on the extent of the damage done.
The 28-year-old has made six appearances in all competitions this season.