Arsenal revealed that the 76-year-old, a close ally of manager Arsene Wenger, had been suffering from pneumonia.
“Peter was taken ill at home on Friday and is currently being treated in hospital. He is making a good recovery,” read a statement from Arsenal.
“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 was appointed as Arsenal chairman in 1982, becoming the third person from his family to assume the role.
His father, Denis, was Arsenal chairman between 1962 and 1982 and his grandfather, Samuel, had two stints in the position in 1929-1936 and 1946-1949.