The 76-year-old, who has been chairman of Arsenal since 1982, had been battling pneumonia before falling ill at his home on Friday.
A club spokesman 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 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.
A protest was held by a small group of Arsenal supporters on Saturday, calling for Hill-Wood to step down from his position.