Officers were shot at from a car this evening, following a deadly shootout outside a police station earlier today.
The suspects escaped the scene but were discovered a short time later in an alley.
Gaziantep is located in the volatile south-east of Turkey.
One would-be terrorist was shot dead but another escaped. It has not been confirmed whether the escaped gunman was involved in the second attack.
Today’s two attacks are just the latest in a series of violent incidents to have rocked Turkey over the last year.
Gaziantep was also the site of a terror attack in May last year, where two people were killed and 22 wounded after a car bomb exploded outside the same police station.
The city of Gaziantep is 65 km (40 miles) from the Syrian frontier and has been a focus of Turkish concerns about the spillover of violence across the border.
A suicide bomb attack on a wedding party in Gaziantep killed more than 50 people on August 20.