Igor Tudor's second-placed side could have cut the gap to PSG to four points with a victory ahead of the defending champions' Sunday game against Lyon.
But instead, Marseille dropped points for the third time in five league outings and could be overtaken by third-placed Lens when they visit Rennes on Saturday.
"Today we weren't good enough to win," admitted Tudor.
"The international break has cost us dearly. There were too many mentally and physically tired players.
"We only had one training session together so I knew it would be tough."
Arnaud Nordin finished off a quick counter-attack to give mid-table Montpellier a 12th-minute lead after a brilliant burst from Wahbi Khazri.
Marseille levelled shortly before half-time as Matteo Guendouzi stroked home a penalty awarded for handball.
But OM created little and Khazri went close to a winner for Montpellier midway through the second period when he was denied by home goalkeeper Ruben Blanco.
Marseille dominated possession late on but could not find a goal which would have given them renewed hope of a first league title since 2010 after PSG's shock home loss to Rennes before the international break.