The child, identified only as Amnah, was found abandoned at Kuwaiti Hospital in the emirate of Sharjah early Saturday, Gulf News reported Tuesday.
She had no identification. Hospital officials said her body bore burn and bruise marks.
Police suspected the father tortured the girl.
The father, who was not identified but was described by police as being in his 40s, was arrested at a resort in the neighboring emirate of Fujairah, police said Monday.
Officials said the man's family tipped the police as to his whereabouts. He was wanted in several emirates on a variety of charges, police said.
Amnah's mother is believed to be an illegal immigrant from Ethiopia who has left the UAE, officials said. The child is in the care of a social services center and is expected to be reunited soon with her family.