San Diego County jail records show Jose Manuel Navarrete was being held on US$100,000 ($139,000) bail for investigation of child endangerment. He was set to be arraigned on March 30.
It wasn't immediately known if he had a lawyer who would speak on his behalf.
Witness Lori Ortale told KSWB-TV she heard a woman yelling "Jose, stop" before a man jumped the fence and through the elephant enclosure.
"These guys right away were saying, 'That elephant is going to charge,' and it did," Ortale said.
"We told him to get out and he turned around and he saw it thankfully just in time," said Jake Ortale, who also witnessed the incident. "He runs, throws his baby through the gate and it's seconds from hitting him. He jumps through the gate, falls on the ground and then it roared."
"The baby starts crying and people were just mad at this guy," he said.
After Navarrete's arrest, the child went home with her mother, police said.
- Associated Press