Journalists at Celtic Park for the game reported seeing the fan lash out at the 18-year-old French youngster shortly after Edison Cavani scored a penalty to put PSG 3-0 up.
Mbappe, who is considered one of European football’s top talents, moved to the big-spending Parisian club in the summer on an initial loan deal from rivals Monaco, who helped win the French League last year.
Darryl Currie, who was covering the game for BT Sport, appeared to confirm the incident in his half-time analysis, claiming that fans near the one who allegedly confronted Mbappe were furious.
Booing was heard as the fan was led away by stewards and police.
The incident, which occurred when Celtic were 3-0 down to the French side in their Champions League Group B opener, was not captured live by TV cameras at Celtic Park.
Brendan Rodgers’ side had already suffered a bad night at the office, after goals from Mbappe, Cavani, and the world’s most expensive player Neymar, had put PSG in the driving seat.
Celtic have not had their problems to seek with UEFA, being fined almost £250,000 by the governing body in just ten years, for a variety of offences during European games.
The club’s most recent run-in with UEFA’s Disciplinary Body saw them paying over £20,000 after the display of a paramilitary style banner in their qualifier against Northern Irish club Linfield.
The previous fines, which have often been a result of actions by the club’s controversial supporters group the Green Brigade, range from political banners to the use of pyrotechnics.