Neymar was signed by PSG for a world record 222 million euros ($260 million) from Barcelona previous year.
Neymar may not be able to influence PSG's results on the pitch, but Henrique is adamant the 26-year-old will be able to play a pivotal role from the stands while he recovers.
A spokesperson for the Brazilian football federation confirmed the operation was a success.
"An assessment will be conducted in six weeks in order to determine the possible date of his return to training".
Brazil team doctor Rodrigo Lasmar, right, and French doctor Gerard Saillant, representing PSG, speak after the surgery.
Neymar is ruled out of Tuesday's Champions League last-16 second leg against Real Madrid and now faces a battle to regains sharpness ahead of the World Cup.
Earlier, Paris newspaper L'Equipe reported that PSG believe Lasmar lied about Neymar's condition.
PSG coach Unai Emery says the club are working hand in hand with Brazil to ensure Neymar has every opportunity to recover as quickly as possible from the operation and prepare properly for the tournament in Russian Federation.
Amid reports of tensions between PSG and Brazil's footballing authorities over Neymar's medical treatment, PSG insisted that it would be in charge of his recuperation.
They said: "Neymar is already in his room".
"There is absolutely no split, despite what was written". "In six weeks we will make a new evaluation", Rodrigo Lasmar said after performing the operation.
"Re-education will begin immediately under the direction of a club physiotherapist".
"The World Cup begins here today, with this operation", said fan Iago Coura, 24, who came to the hospital with three friends.