Balotelli told members of the Nice delegation that monkey chants had been aimed at him, and the LFP told AFP "the matter will be studied by the Disciplinary Commission" on Thursday.
The former Manchester City and Liverpool striker was booked by referee Nicolas Rainville for a gesture towards the crowd which he said had been provoked by the abuse.
The LFP said it would have further information following a study of the match delegate's report on Monday.
In a statement on the official Nice website, president Jean-Pierre Rivere said Balotelli had the club's full backing.
"We took the time to consult with the different parties before speaking about this," he said.
"We deplore the fact that Mario had to suffer another instance of racism. It's inexcusable, and you have to remember that this isn't the first time since he has joined our league. He has our full support.
"As Olivier Dall'Oglio, the Dijon coach, said, we aren't protected from 'one or two morons.' This is a sentiment that we share and Mario didn't wish to add any more to that after the match.
"The Dijon fans are not used to this. I have no reason to cast into doubt the good faith of the directors at Dijon, nor to heap this on them, given that they are just as much the victims of this incident, which could happen anywhere.
"We are all convinced of the same thing, racism has no place in a football stadium, nor anywhere else."
Balotelli, in his second season in France, was subjected to racist abuse by Bastia fans last season, with the LFP Disciplinary Commission handing the club a suspended one-point deduction and ordering the closure of one of their stands for three games.