Camara found the back of the net two minutes into added time to cancel out Radamel Falcao's first-half opener as Monaco stayed second on 19 points, behind Paris St Germain on goal difference.
PSG take on Bordeaux on Saturday.
Montpellier, who also held PSG in their previous game, are 10th on nine points.
Monaco were defeated 3-0 by Porto in the Champions League on Tuesday and their limitations were once again exposed on Friday.
Montpellier dominated for long spells in the first half, shooting 10 times, but Monaco were more clinical.
On their first shot on target, they took the lead as Falcao latched onto a Rony Lopes cross for his 12th league goal of the season in eight games.
Leonardo Jardim's team were more focused after the break as they held on to their minimal lead.
But Camara, who came on in the 72nd minute, headed home to secure a deserved draw for Montpellier.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
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