Cpl. Sandra Rogers, a 27-year veteran of the force, died at a hospital.
A spokeswoman for the South Carolina Law Enforcement Division identified the suspect as Joshua Tremaine Jones, 26. His address and specific charges were not given.
He was arrested on Youman Street in Batesburg, S.C., and is now in the Aiken County custody, SLED spokeswoman Kathryn Richardson said.
Lt. David Turno confirmed that one officer was shot at 7:30 a.m. and has been taken to Aiken Regional Medical Centers.
The incident occurred near Eustis Park on Edgefield Avenue.
Officers at the scene say they were responding to a suspicious activity call in the park.
Responding officers heard gunshots and then saw the metallic blue BMW leaving the scene.
A neighbor said she heard three shots fired. The park has been sealed off.
Officers at the scene late Saturday morning said they haven’t gotten over last month’s fatal shooting of Master Public Safety Officer Scotty Richardson.
“It’s like a horrible nightmare playing over in front of us,” Sgt. Aaron Dowdy said. “I’m still wearing a Richardson band on my wrist.”