The 76-year-old leader of the Catholic Church in Scotland was said to be «comfortable» and settled in the Victoria Infirmary. But he was expected to be kept under close observation for the rest of the weekend.
A spokesman for the Archdiocese of Glasgow said the cardinal will need time to recover before returning to his busy schedule.
The cardinal was taken to the infirmary by ambulance Friday after the heart attack at his home in the city. He was said to be conscious, although in some discomfort.
A spokesman for the cardinal said: «He was well enough to joke with the nurses at the hospital. One introduced herself as Jane. He replied to her: ´I´m Tarzan.´»
Cardinal Winning became a cardinal in 1994 and has made the voice of the Catholic Church more high profile than ever in Scotland, BBC said.