Sky Sport Italia reported that Bove was transported to the Careggi Hospital near the Stadio Franchi in Florence and that he was breathing on his own and had regained consciousness.
A Serie A spokesperson said later that the match was suspended and would be postponed to a later date.
Later, in a statement from the club and the Careggi University Hospital Company, they said: "The footballer Edoardo Bove, who was rescued on the pitch following a loss of consciousness during the match is currently under pharmacological sedation and hospitalised in intensive care.
"Bove arrived at the emergency room in stable hemodynamic condition and the first cardiological and neurological tests performed excluded acute damage to the central nervous system and the cardio-respiratory system. He will be re-evaluated in the next 24 hours."
Play was halted at the stadium to review a potential VAR check on a disallowed Lautaro Martinez goal when the 22-year-old, seemingly bending down to take off his boot, suddenly collapsed in the 17th minute.
Medical personnel rushed onto the pitch, with the Fiorentina players forming a ring around Bove, who arrived at the club on loan from AS Roma in August.
After Bove was taken away in an ambulance, the referee asked the players to leave the pitch and return to the dressing room.
Inter chairman Giuseppe Marotta stated that postponing the match was an easy decision.
"Football is a community, so naturally when these situations happen, all the players and the referee worked together to help and it was a spontaneous decision to abandon the game," he told Sky Sport Italia.
Support for Bove poured in from other Serie A clubs.
"We all are with you Edoardo!" Juventus posted on X where league leaders Napoli said: "Come on Edoardo, we are with you!".