The Argentine, linked to Barcelona when his contract expires this summer, has seen two Champions League last-16 exits in his two seasons at the club, BBC Sport reported.
Whistles could be heard as his name was announced beforehand, although some fans chanted his name in support.
Lyon forward Bradley Barcola scored the only goal as PSG were booed off.
The game kicked off 10 minutes late as Lyon’s bus could not fit under a bridge so they had to drive around the capital.
Alexandre Lacazette had earlier struck a post with a penalty for the ninth-placed visitors.
Kylian Mbappe, PSG’s all-time top scorer, almost rescued a point late on, but his shot was saved.
The perennial French champions are now only six points above Lens and Marseille with nine games left.
PSG have lost seven of their 18 matches in all competitions since the end of the World Cup, having been unbeaten in all 22 games before the break.
Messi is in talks with PSG about extending his contract, but Barcelona have also approached him about a return to the club where he spent the bulk of his career. He has scored 29 goals in 67 games for the club.