Police arrested Rollen Oliver, 21, after finding a gun in his possession shortly after the Sunday shooting, police Chief Robert White said.
Oliver was being held in Denver's jail without bond and could face first-degree murder charges, The Denver Post reported.
Denver police officer Celena Hollis was shot in the head shortly after 8 p.m. while trying to break up a fight between two people. She was declared dead at a hospital.
Hollis was a seven-year veteran of the Denver police force who was originally from Detroit and was married with two children.
"She was easy to get along with and always had a smile on her face and happy to approach each day," said Lt. Ron Thomas, a board member of the Denver Black Police Officers Organization.
Police said they don't believe Oliver targeted and intentionally shot Hollis. They are investigating whether the man is a gang member and if the fight was gang-related.
The weekly City Park Jazz concert was a tribute to Charlie Burrell, a jazz bassist who also plays with the Denver Symphony Orchestra. Purnell Steen and Le Jazz Machine also performed.