The 76-year-old's heart attack followed a bout of pneumonia, the club said.
A statement from the club read: "Peter was taken ill at home on Friday and is currently being treated in hospital. He is making a good recovery. The club wishes Peter a full and speedy return to health and our thoughts are with him and his family at this time."
Hill-Wood has been chairman of the club since 1982, and is a former vice-chairman of the Hambros Bank.
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.
Source: PA
Source: PA