A spectator ran on to the playing surface at Celtic Park and swung a leg in the direction of Mbappe but the France international was able to stay out of the way.
The invader was then led out of the stadium by security staff.
Such an incident could mean disciplinary action from UEFA for Celtic, with the supporter able to break through the measures set up to prevent pitch encroachment.
Unfortunately for Celtic, their players struggled to get any closer to Mbappe than the fan.
The 18-year-old scored the second of a three-goal flurry in the first half as PSG went into the break with a convincing 3-0 lead.
Once again, both of his new strike partners - Neymar and Edinson Cavani - were also on the scoresheet.
Mbappe was substituted in the closing minutes for Giovani Lo Celso with Mikael Lustig's own goal having put the Parisians' four goals to the good.
Cavani added a fifth immediately after his exit on another excellent evening's work for Unai Emery's side.