The teenager, whose name was not released, was arrested Sunday night at an apartment near where Bryan Lockley's body was found Saturday.
The teen was raised with Bryan and often lived in the same apartment in a rough South Los Angeles neighborhood.
"They're very close by all accounts," Capt. Kenneth Garner said. "We do know that they had had some rivalry in the past, and so that may play a part in this."
Bryan's sister, 24-year-old Ramona Reese, said she spoke with the 14-year-old by phone Monday.
"He was upset and said it was an accident," she said. "I want to talk to him personally, see eye to eye. He's my cousin. I love him regardless of anything."
People in the neighborhood said they were stunned by the brutality of the killing.
"It's unbelievable that it would happen like that," said Bruce Edwards, 41, who runs a market. "Everyone around here is walking with a question mark above their heads."
Bryan's body was found by a woman digging through a trash bin for recyclables. He died of a shotgun wound to the chest, and police believe the teen carried Bryan's body in a garbage can to the trash bin, Garner said.
Police searched for the gun
Bryan, a sixth-grader at Bret Harte Middle School, was a "good kid," Garner said.
On Saturday, his mother, Francine Lockley, was to be reunited with him that day after graduating from a treatment program for addicts. Instead, she returned home to find her apartment filled with police officers.
Lockley, 44, had given birth to Bryan while in prison, and told the Los Angeles Times she was hoping to create for the two of them "a normal life in society - something that we never had because I was in my addiction."
"I went out and got a job and I was just ready to be the mother that I was meant to be," she said.
By Daisy Nguyen