The capital club could have overhauled Olympique Lyonnais with a victory at the Stade Louis II but they paid the price for the profligacy of Edinson Cavani adn Ezequiel Lavezzi
Surprise defeats for title rivals Marseille and Lyon earlier in the weekend had opened the door for the champions to reclaim top spot.
But, despite creating several clear openings, Laurent Blanc's side were unable to find the breakthrough without top scorer Zlatan Ibrahimovic.
Leonardo Jardim's men were far from the all-action outfit that defeated Arsenal 3-1 in the Champions League on Wednesday, but did enough to hold on for a draw that moves them into fourth position.
PSG were the better side for much of the contest and remain the only team unbeaten this season in matches against Ligue 1's top five.
But the champions were either too intricate, or inaccurate in front of goal, meaning they stay second, a point behind leaders Lyon. The teams meet again at the Parc des Princes on Wednesday in the Coupe de France.
Despite being without a number of key players, including the suspended Ibrahimovic and the injured Lucas Moura, the visitors soon settled into their preferred pattern of play, dominating position, albeit at a pedestrian pace.
The hosts appeared equally comfortable to allow their opponents the ball, dropping deep to prevent space in behind.
A smart run from Ezequiel Lavezzi created the first real opening in the 16th minute. The Argentinian raced through to collect a ball over the top before teeing up Edinson Cavani to drive at goal from 15 yards, but Danijel Subasic was equal to it.
This brought the match to life and Lavezzi should have broken the deadlock in the 25th minute, only to scuff his volley horribly wide from six yards after Maxwell's lofted ball was nodded down by Blaise Matuidi.
As if encouraged by surviving such scares, Monaco improved, but found Joao Moutinho to be just as wasteful in front of goal, failing to make clean contact from inside the box following good work from Yannick Carrasco in the 36th minute.
There was still time for Cavani to squander another good opportunity after being found in the box by a combination of Matuidi and Javier Pastore in stoppage time, prompting Blanc to smack the dugout in frustration.
The hosts made the brighter start to the second half, but PSG had the first chance, as Pastore and Lavezzi exchanged passes on a 53rd-minute counter before the former fired straight at the goalkeeper.
Pastore combined with Marco Verratti to go through on goal nine minutes later, but on this occasion lifted his effort just wide as Subasic dived at his feet.
The pace and purpose disappeared from PSG's play after this and Monaco were happy to contain their visitors.