Barnes was shot in the head July 25 while working at the Raymond Rosen Manor housing project at 24th and Norris Streets, in North Philadelphia, and died Aug. 5.
Police suggested after the crime that the shooting may have been a case of mistaken identity.
On Sunday, police obtained an arrest warrant for Simmons after they came to believe that he was involved in the slaying, said Lt. Frank Vanore, a Philadelphia police spokesman.
Yesterday's arrest began to unfold when police in Whitehall stopped a 2003 blue Chrysler Town and Country minivan driven by Kaream Bundy, 32, of Philadelphia, who was pulled over for speeding, said patrolman Desmond Lyons.
Whitehall Officer Daniel Price asked Bundy for his license, and he said he didn't have it, Lyons said.
Price asked Simmons, who was in the passenger seat, for his license and he gave it to the officer, Lyons said."Standard procedure when that happens is to ask the passenger if they have a license so that they can take the car," Lyons said.
Price ran both names through the national crime database, which found warrants for both - Simmons in the July slaying and Bundy for a parole violation, Lyons said, adding that both were arrested without incident and charged with being fugitives from justice.
Simmons and Bundy are awaiting extradition to Philadelphia, Lyons said.
"The news today was great; it was just a huge sigh of relief," Rachel Barnes said.
"My uncle was like a father to all of us; anything you needed from him you would get it. We're just dealing with it and coping the best way we can."