The man was hospitalized and is listed in critical condition.
Initial reports indicated the girl had been thrown from a second-story window, but that turned out not to be the case.
The call came in at 2:05 p.m. Friday as an assault with a deadly weapon call, said Los Angeles Police Department Officer Drake Madison.
He says a small fire in the apartment was quickly contained and a 25- to 30-year-old man who had self-inflicted knife wounds was taken into custody. Torres was arrested on suspicion of murder and is being held on $1 million bail, according to online records.
According to the Los Angeles Fire Department, they received a call about a structure fire at 2:31pm at 13100 block of Vanowen Street, North Hollywood.
The LA Daily News reported that the man locked himself in his North Hollywood apartment before he set fire to it. Police discovered the suspect in an alley next to the apartment on fire with a steak knife in his chest.
Carmona said investigators found evidence the suspect had used drugs - possibly methamphetamine.
A man in North Hollywood, California, allegedly stabbed and killed his 13-month-old infant daughter and set his apartment on fire and jumping from a second-floor window after stabbing himself in his chest.