The 76-year-old, who has been chairman of Arsenal since 1982, suffered the heart attack following a bout of pneumonia.
A spokesman for the club said: "Peter is recovering well in hospital and there is a good prognosis. We are hoping he will make a full and speedy return."
Hill-Wood was taken ill at home on Friday and moved to hospital for treatment.
He is the third member of his family to serve as Arsenal chairman, following on from his father Denis (1962-1982) and his grandfather Samuel, who had two separate spells in the role between 1929 and 1936 and from 1946 to 1949.