The 76-year-old fell ill on Friday following a bout of pneumonia, and is being treated at hospital - but the club has revealed he is making a "good recovery"
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 in full read:
|GIROUD TO THE RESCUE|
|5/1||Olivier Giroud is 5/1 with William Hill to open the scoring against Olympiakos|
"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 leaders Manchester United.