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Another spokesman, Deputy Charles Scudella, said Winston had posted bond Monday night and would be released. He did not know how much the bond was.
Employees at the Sun City West Animal Hospital northwest of Phoenix reported that Winston hit the Chihuahua, named Bella, in the head three to five times with his fist.
The dog survived, but had to undergo corrective surgery.
"The eye was put back in and stitched," Scudella said. "It's a wait-and-see if the dog still gets use of the eye."
Two veterinarian technicians who said they witnessed the incident told the sheriff's office that Winston was extremely frustrated with the dog because it was uncooperative and aggressive during a visit for spay surgery.
"We trust our vets with those that we love most," Maricopa County Sheriff Joe Arpaio said. "Most vets are good people, they love animals. I just hope this is an isolated incident, not just with this vet, but with any vet."
Winston also faces a theft charge from an incident earlier this year. Hospital employees said Winston charged a client $80 for medication he didn't give a Neapolitan Mastiff after the dog became uncooperative.
A call to the animal hospital was not immediately returned Monday.