"We're in a bit of a sombre mood, especially among the younger ones because obviously he's their manager," Hessenthaler told BBC Radio Kent.
"He's had an operation and at the moment he's stable. We're all worried the first team boys as well."
The Gills boss added: "He's a fantastic coach so we hope to see him back at the club soon."
Hare was taken ill after he returned home from watching Gillingham's next opponents - Oxford - play at Southend.
He is currently being treated at the William Harvey Hospital in Ashford.
As a result this weekend's youth team game at Brighton has been called off.
Source: BBC Sport
Source: BBC Sport