"The club's medical staff is satisfied with the way the operation went but are not available for further comment," a statement on the PSV website said.
"The club makes an urgent request to respect Phillip Cocu's privacy and wishes him much fortitude on the road to a healthy recovery. He will need all his energy and strength in the time ahead for his recovery process."
Cocu will be off work for an undisclosed period of time and his assistant Ernst Faber will take charge of the team on a temporary basis.
The 43-year-old Cocu's young PSV side started the season slowly but have improved markedly in recent months, moving up to second in the standings after eight successive wins.
PSV, who are six points behind leaders Ajax Amsterdam, host Groningen on Saturday.
Cocu is a former Dutch international midfielder who earned 101 caps and played for AZ Alkmaar, Vitesse Arnhem, PSV and Barcelona.
- Sports & Recreation
- Phillip Cocu