The match between hosts Bordeaux and Rodez was halted midway through the first half when a home fan approached the pitch and pushed over Rodez player Lucas Buades, who had just put the away team in front.
The match was halted and did not restart.
The source said the alleged aggressor was one of those taken into custody. He was described as a 45-year-old man and a resident of the city of Annecy by local Bordeaux newspaper Sud Ouest.
Police allege that he invaded the pitch and "violently pushed" Buades, who was left concussed according to the referee.
The other three individuals to have been arrested, according to the newspaper, are two men aged 29 and 30 who also invaded the pitch, and a 47-year-old who allegedly headbutted a steward.
The French league (LFP) will meet on Monday to discuss the incident which overshadowed the final night of the Ligue 2 season.
A crowd of over 40,000 gathered in Bordeaux hoping to see their team secure promotion back to Ligue 1, a year after they were relegated from the top flight.
Le Havre secured the second-tier title to clinch a return to Ligue 1 after a 14-year absence, while Metz beat Bastia 3-2, a result which left them second, three points ahead of Bordeaux and with a better goal difference.
Bordeaux will therefore hope to be given the chance to replay the game, which also concerns the other end of the table.
Rodez are in the relegation zone, but a win against Bordeaux would secure their safety and relegate Annecy instead.
