An on-site vet tried to save Henry, but he died a few minutes later.
An X-ray showed Henry had two broken ribs and a punctured lung.
PetSmart said Zarate has been suspended pending the outcome of an ongoing investigation.
"We are heartbroken by the loss of Henry. Nothing is more important than the health and safety of pets, and we take full responsibility for the pets in our care," PetSmart said in an email to KGO. "We are conducting an internal investigation and will take immediate action based on our findings. Additionally, we are working with the local authorities.
"Any incident of animal cruelty goes against everything we believe as a company and as individual pet parents. No words can express our deep sorrow for the family, and we will continue to work with the pet parent during this difficult time."
Family spokesperson Marisa Mendoza told KVTU Zarate is used to handling smaller dogs because he has a Chihuahua at home.
"He's kind. He loves animals. The animals love him," Mendoza said. "He was crying a lot.
"He would never hurt an animal," she said.
Police said Zarate is cooperating in the investigation. He posted bail Monday and is due in court next month.
The dog's remains are in custody of the Peninsula Humane Society -- SPCA. A necropsy was conducted Monday. Results may take at least a week.