The Corsican club said in a statement that the unnamed supporter, a season ticket holder in his 40s, had turned up at the Armand Cesari stadium on Tuesday and confessed to his actions.
Bastia had put out an appeal for information on local television after reviewing broadcast images that picked out an individual making monkey chants during the warm-up.
Balotelli posted a message on his Instagram page the day after leaders Nice drew 1-1, saying the incident was a "real shame".
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"I have a question for French people...Is it normal that Bastia supporters make monkey noise and 'uh-uh' for the whole game and no-one of the "commissions discipline" say nothing?," wrote the player, on loan from Liverpool this season.
"So is racism LEGAL in France? Or only in Bastia?," he added. "Football is an amazing sport...those people like Bastia supporters make it horrible."
The French League (LFP) has said it will investigate the incidents in its next disciplinary commission meeting on Thursday.
It also sent footage from BeIN Sport TV channel, showing some Bastia fans racially abusing Balotelli, to its disciplinary commission.
Bastia were docked two points by the LFP in the 2007-08 season after fans racially abused a Libourne St Serin player during a Ligue 2 game.
(Reporting by Alan Baldwin in London, editing by Pritha Sarkar)
