The 88-year-old was admitted to Madrid's Gregorio Maranon Hospital's intensive care unit where he is being kept in an induced coma in the coronary unit.
A medical report from the hospital said he was "clinically and haemodynamically stable", but that his condition remained "serious".
According to reports in Spain, Di Stefano was on a street close to the Bernabeu when he had the heart attack. The hospital said the emergency services were able to stabilise him.
The medical report, which Madrid published on their official website, said: "The patient is currently in the coronary unit at the Gregorio Maranon Hospital.
"He is under sedation, with endotracheal intubation and artificial ventilation, and is being subjected to the relevant clinical trials.
"The patient is clinically and haemodynamically stable, but his condition remains serious."
Di Stefano underwent a quadruple aorta-coronary bypass with a pacemaker implanted in December 2005 after suffering a myocardial infarction.
He was voted European player of the year in 1957 and 1959, is most associated with Real Madrid and was instrumental in their domination of the European Cup during the 1950s; the club won the trophy in five consecutive seasons from 1956.
Along with Francisco Gento, he was one of only two players to play a part in all five victories and he is the honorary life president of the 32-time Spanish champions.
Di Stefano played international football mostly for Spain - scoring 23 goals in 31 appearances - but he also played for his native Argentina and Colombia.