The Fiorentina midfielder suddenly collapsed on the pitch when 16 minutes had been played.
Players and spectators watched in horror as medical personnel attended to the 22-year-old Bove, who was then taken to hospital by ambulance.
Both teammates and opponents openly wept and comforted each other on the pitch.
The match was abandoned and will be replayed at a later date.
According to Sky Italia, Bove regained consciousness in the ambulance on the way to the nearby hospital in Florence.
Bove's parents and girlfriend arrived at the hospital together with Fiorentina's coach Raffaele Palladino and several of his teammates, as well as the mayor of Florence, writes AP.
Many supporters also gathered outside the hospital.
"The initial cardiologic and neurologic tests do not indicate any acute injuries to the central nervous system and cardiovascular system," the club and hospital said in a joint statement.
Fiorentina was struck by sorrow and pain in 2018 when team captain Davide Astori died in his sleep the night before an away match against Udinese. He was 31 years old.
