The forward has been linked with a move back to former club Barcelona.
"Paris St-Germain notes that Neymar Jr was not in attendance at the agreed time and place. This was without the club's prior authorisation," read a statement.
"The club regrets this situation."
In an interview PSG's sporting director Leonardo said: "Neymar can leave PSG, if there is an offer that suits everyone."
He added that there had been "very superficial contact" from Barcelona.
"But to date, we do not know if anyone wants to buy it or at what price. PSG wants to rely on players who want to stay and build something big."
Brazilian media quoted Neymar's father, Neymar Sr, as saying that PSG "were aware" that the forward was set to miss training on Monday because of charity commitments.
"The reason was known and planned for a year as part of his activities for the Neymar Institute," he told Fox Sports Brazil, “We couldn't postpone them and he will return [to PSG] on 15 July."
Neymar joined PSG from Barcelona for a world record 222m euros (£200m) in August 2017. He has scored 34 goals in 37 league appearances