The 15th-ranked Monfils, who beat Rafael Nadal in the semifinals, had broken the sixth-ranked Tsonga to go up 1-0 and was down 0-15 in the second game on Saturday when play was stopped.
Organizers announced play would be halted "for a while" because of concerns the slippery court was too dangerous for the players. They did not say when play might resume.
As fans waited in their seats, workers with brushes could be seen scrubbing the edges of the court. The fog, which occurs during the cooler months at night in the Gulf, drifted past the stadium in downtown Doha.