The French football federation's disciplinary commission added a suspended two-match ban to its punishment.
"I was wrong but I don't have cockroach blood", Neymar later said when commenting on his behaviour during the incident, with TMZ explaining that the saying the footballer used essentially means that "he won't back down from people when they cross a line".
While having to plan without Neymar at present, PSG have stated their intention to appeal the sanctions handed out to the South American.
Neymar exchanged a few words with the supporter then raised his hand to him.
According to the Associated Press, PSG players Gianluigi Buffon and Marco Verratti also were verbally abused by the same fan, though they ignored him.
PSG coach Thomas Tuchel criticised Neymar for the spat and the Brazilian player later apologised.
Neymar's suspension will not start until Monday so, in theory, he could play away at Angers this weekend before missing the games against Dijon and Reims. The Brazil star will also miss the first match of the 2019-20 season.
He was banned for three European games for insulting match officials on social media after PSG were eliminated from the tournament by Manchester United and will miss half the group stage next season.
He became the most expensive player in the world when he moved from Barcelona to PSG for 222million euros (NZ$378.26m) in 2017.
UEFA suspended Neymar on April 26, meaning he will miss the first three group matches of next season's Champions League, but he has chose to appeal.