Officials say they are searching for a second assailant.
A gunfight broke out in front of the police compound and ambulances were sent to the scene, television channels reported.
Deputy Prime Minister Numan Kurtulmus told reporters in parliament that a police operation was underway to locate the second attacker.
One police officer was wounded in the clash and was taken to hospital for treatment, the Gaziantep governor’s office said.
Eyewitnesses said a dead person, presumed to be the would-be attacker, was lying on the ground in front of the police station, Dogan news agency said.
Turkey is still reeling from an attack on New Year’s Day in which a gunman killed 39 revellers inside a popular Istanbul nightclub. Islamic State claimed that attack.
Gaziantep police station was previously targeted on May 1 when two police officers were killed and 22 people wounded in a car bomb attack, which at the time was linked to Islamic State.
The city of Gaziantep is 65 km from the Syrian frontier and has been a focus of Turkish concerns about the spillover of violence across the border.
Four days later, Turkey’s army launched an operation with Syrian rebels to drive Islamic State away from its southern border.