The fire was reported around 11 p.m. on the 11500 block of West Riverside Drive.
Firefighters discovered the Osmanhodzic's body after putting out the flames.
"The responding Los Angeles Police Department units examined the scene and determined that the death was of a suspicious nature. They notified North Hollywood homicide detectives who responded to the scene and determined that the incident is going to be handled as a homicide," said LAPD Lt. Alan Hamilton.
Police said the Osmanhodzic's boyfriend had returned from a store, confronted the suspect inside the house and chased him several blocks.
By the time he returned, the house was on fire.
Family and friends stopped by Osmanhodzic's Sunday to salvage what they could. They're still in shock that just days ago she was out with friends and looked forward to her wedding in September.
"I don't know why someone would do this to her," said one of Osmanhodzic's friends. "This is just devastating for us right now."
The suspect is described as a Latino man in his 20s with a stocky build.
He is about 5 feet 8 inches tall and was wearing black shorts, a blue shirt and a backwards baseball cap. Authorities released a composite sketch of the suspect Sunday afternoon.
Anyone with information is asked to call police at 1 (877) LAPD-24-7 or 1 (877) 527-3247.