The surgery was carried out on Thursday after the 43-year-old complained of back pain, with the club explaining that the tumour is likely to be benign.
Technical director Marcel Brands is set to make a further statement on Cocu's recovery on Friday, with assistant coach Ernest Faber taking control of first-team selection duties for the time being.
A statement on PSV's website read: "After investigation following back pain Phillip Cocu was recently diagnosed with a tumor in his back, for which he has undergone surgery.
"The executive medical team and the medical staff of PSV are satisfied with the conduct of the operation, but are not otherwise available for comment.
"(Cocu's) duties are performed by the other members of the technical staff.
"Assistant coach Ernest Faber will act as an outside point of contact for all sporting matters surrounding the selection."
PSV have won eight games in a row to move up to second, six points behind Ajax.
