A looping 52nd-minute header from Layvin Kurzawa, allowed to stand despite suspicions of offside, looked set to give Claudio Ranieri's men three points at Stade de la Mosson.
However, struggling Montpellier, 17th in the table, levelled 16 minutes later when Milan loanee M'Baye Niang marked his first league appearance for the club with a goal.
Niang, who also scored on debut against Rodez in the Coupe de France on Sunday, saw a penalty saved by Danijel Subasic following Eric Abidal's trip on Remy Cabella, but the forward reacted quickly to slot home the rebound and earn a precious point.
Despite the presence of Radamel Falcao, making his first league start since 24 November, Monaco failed to find a winner.
The men from the Principality have now dropped points in two consecutive Ligue 1 fixtures and could be leapfrogged by Lille, who host Reims on Sunday.
PSG, meanwhile, travel to Ajaccio on Saturday and will hope to extend their advantage at the summit, which currently stands at two points.
