Andres Tafoya, 30, was watching his 2-month-old daughter on the morning of November 1 while the child's mother was at work.
Tafoya is believed to have punched the baby multiple times to the head, causing injury, police said.
Tafoya assisted in transporting the baby to a hospital, where she was admitted in critical condition with head and skull injuries. Tafoya left the hospital before officers arrived, police said.
Police located Tafoya on Sunday and arrested him on charges of attempted homicide and causing willful harm/injury to a child. Tafoya was held at the Santa Ana Jail.