They said Sunday that Tran Hoai Thuong, 33, who is being investigated for "deliberately inflicting injury," was arrested after the child was brought to a hospital unconscious and with skull damage and broken limbs on Saturday night.
The hospital informed the police immediately.
Investigators found that the child's mother, a 22-year-old woman, had separated from her husband in February just after she delivered.
She then entered into a relationship with Thuong and moved in with him along with her daughter into an apartment in Da Lat.
Thuong told the police that he was constantly angry with the child because she kept crying and refused to drink formula and had beaten her on three occasions this month.
When they were taken into custody, both he and the child’s mother tested positive for narcotic substances.