Officers and firefighters responded shortly after 4:30 a.m. to the 100 block of South Fifth Street, just south of Whittier Boulevard, according to the Montebello Police Department.
"Upon arrival, officers were contacted by a male adult and a female adult with severe burns to the front of a residence that was fully engulfed on fire," police said in a statement.
The blaze was quickly extinguished by the Montebello Fire Department and the two injured victims were transported to a hospital.
A deceased victim was found inside the residence, prompting a joint investigation by police detectives and arson investigators, officials said. The age and identity of the deceased person were not immediately confirmed.
"There are no outstanding suspects in this investigation and there is no danger to the community," the police statement said.
At a news conference, Montebello Police Chief Luis Lopez confirmed that investigators were looking into reports of possible domestic violence connected to the fire.
No additional details about the cause of the blaze were available.