The £7.8m fee relates to a "loyalty bonus" which was included in Neymar's contract, and paid to the player, when he penned a five-year extension in October of last year.
Neymar's had an immediate impact with his new club, accounting for three goals and three assists in two Ligue 1 appearances for PSG.
Spanish Club Barcelona has filed a legal lawsuit against Paris Saint Germaine Striker, Neymar.
The 25-year old joined PSG in a world record fee of 222m euro (£200m) after PSG accepted to trigger his release clause.
After scoring twice on his home debut for PSG - a 6-2 thrashing of Toulouse on Sunday - Neymar took aim at the Barcelona board, claiming "there are directors that shouldn't be there".
Paris Saint-Germain have denied any wrongdoing and issued a statement declaring their "surprise" at Barcelona's decision to take legal action against Neymar for an alleged breach of contract.
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La Liga accused PSG of violating Uefa's Financial Fair Play (FFP) rules and Barcelona previously said they would report the French side to Uefa for a FFP breach.
"The club also requests Paris Saint-Germain take on responsibility for the payment of these fees if the player can not do so himself", it said.
If the Spanish Super Cup is a determinant, then it could be said that Barcelona are really missing Neymar as they were lost during both legs of the game.
Neymar did not publicly say he was considering a move to PSG until August 3, the day Barcelona terminated his contract and he signed with his new team. But with them [the board], no. For me, they shouldn't be in charge of Barca.
"To see my former teammates unhappy makes me sad also, because I have many friends [there]. Barca deserve much better, and everyone knows this".
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