The French champions, who had lost two of their last three competitive games, lacked inspiration and head into the mid-season break with low morale.
Laurent Blanc's side, who suffered their first league defeat of the season at En Avant Guingamp last weekend, have 38 points from 19 matches and trail leaders Olympique de Marseille on goal difference.
Arch rivals Marseille will extend their advantage over PSG to three points if they beat Lille at home on Sunday.
Third-placed Olympique Lyonnais, who have 36 points, could take top spot if they win at Girondins de Bordeaux also on Sunday and OM fail to claim all three points at the Stade Velodrome.
PSG failed to create a decent chance while Montpellier did not manage a single shot in a dull first half.
Jonathan Ligali parried away David Luiz's powerful 25-metre free kick as PSG upped the tempo after the break.
In the 64th minute, Thiago Silva's header at the far post was cleared off the goalline by Anthony Mounier.
Edinson Cavani put in a disappointing display and with 25 minutes left was substituted by Jean-Christophe Bahebeck, who brought speed to the frontline, but never came close to scoring.
Zlatan Ibrahimovic was a pale shadow of his usual brilliant self.
PSG were denied a possible penalty four minutes from time when Adrien Rabiot was challenged in the box by Mathieu Deplagne, but three points would have been barely deserved.
(Reporting by Julien Pretot; Editing by Mark Meadows)
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