Officers responded to the 100 block of Ellis Street at about 6 p.m. Tuesday after an anonymous tip came in requesting a wellness check.
It wasn't until hours later that officers received a search warrant and were able to enter the triplex residence. The woman's body was found in the front unit.
Police said it was obvious that she had been murdered, but they did not say how she was killed.
The victim's identity was not released, but the coroner's office described her as a 51-year-old African-American woman.
Investigators said the suspect, whose name was not released, is 49 years old. He was tracked down in Compton, where he was arrested.
Investigators said the killing was the result of a domestic dispute.
Neighbors said the woman lived in the unit with her boyfriend, and that the couple kept to themselves.
"They probably just moved in like two months ago," said neighbor Lesley Mendoza, who said she saw officers towing away a car from outside the residence around 2 a.m. Wednesday.
"They were looking in a car, I know that. They were looking in a car, and possibly a person was there. They started knocking on the doors. Nobody was there," Mendoza described. She said police continued knocking for 20 to 25 minutes before they forced their way in and surrounded the area with police tape.
It's unclear how long the body had been at the home. Neighbors said they never heard anything unusual coming from the unit.
"Nobody heard anything, and if there was any noise, we would have heard, because how quiet it is right now, that's how quiet it is during the day. Even when the kids are playing, it's not even that rowdy. So, if something would have happened, like a gunshot or something, I think somebody would have heard," Mendoza said.
Another neighbor told Eyewitness News that police asked her if she had heard the sound of cement breaking coming from the unit Tuesday night. The neighbor told police she had not heard anything like that coming from the residence.