Hill-Wood was taken ill on Friday while at home, and is still being treated in hospital.
He took over the role as chairman of the club in 1982, and is the third generation of his family to take control of Arsenal, following his father Denis Hill-Wood and grandfather Samuel Hill-Wood.
The Arsenal statement is below in full:
"Everyone at Arsenal Football Club sends their support and best wishes to Chairman Peter Hill-Wood who is recovering after suffering a heart attack, following a bout of pneumonia.
"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."
Arsenal were defeated 2-0 at home to Swansea on Saturday, with the board criticised by fans who staged a pre-match protest, and manager Arsene Wenger calling for his side and the fans to "stick together" after the game, as they slipped to 10th position, 15 points behind Premier League leader Manchester United.