A spokesman for La Paz Hospital said: "Ballesteros remains in a serious and stable condition and will undergo a new operation."
He said the tumour was in a particularly difficult area for surgeons to reach, adding: "It is located in an area that requires a very thorough approach of great complexity."
Doctors said the 51-year-old is suffering from an oligoastrocytoma - a tumour that affects two types of brain cell and spreads diffusely inside the brain cavity.
Dr Geoff Pilkington, a tumour expert at the UK's University of Portsmouth, said the tumour was very difficult to eradicate but survival time could be improved by radiotherapy followed by chemotherapy.
He said it was difficult to say how long he might survive without knowing more about the tumour, which will have been classified from one to four on a grade of seriousness.
The hospital declined to reveal the tumour's grade.
"I think it's going to be at least a three because the mixed tumours usually are," he added. "They generally develop into a high grade tumour from which a patient will eventually die. This is not good. The likelihood is that he will die from the tumour at some stage."
The star, who collected 87 titles before knee and back problems forced him to retire last year, underwent major brain surgery earlier this month.
He was admitted to hospital and the brain tumour diagnosed on October 6, after he collapsed and briefly lost consciousness at Madrid airport.
The first operation was followed by a second round of surgery to ease a build-up of fluid on his brain after he took a turn for the worse.
Ballesteros won the British Open in 1979, 1984 and 1988 and became the first European to win the Augusta Masters in 1980, a title he repeated in 1983.