The match will resume on Monday with the winner set to take on Stan Wawrinka in the quarter-finals.
Federer had beaten Monfils three times previously at Roland Garros and each time he went on to reach the final. But he had lost their last two matches, both on clay, in the Davis Cup final last November and in Monte Carlo in April.
Both men looked up anxiously at the dark clouds overheard as they came out for their 13th career matchup and it was Federer who looked the sharper as the tie got underway, Monfils clearly perturbed by the cold, windy conditions.
Federer, whose only title at Roland Garros came in 2009, took the first set on a single break of serve in 29 minutes.
Monfils, though, started to settle in the second and he broke serve to take a 4-1 lead.
Federer broke back with some superb shot-making but he was unable to draw level as Monfils staggered him with a series of haymakers.
The match referee then called both men to the net and they all agreed that the light was too poor to continue.