The two attackers, who also died, tried to ram a car into the building in the town of Pinarbasi, Interior Minister Idris Naim Sahin said.
A bomb in the vehicle went off shortly after clashes with security guards.
Sixteen civilians and another police officer were also injured, some seriously, reports said.
Some of the people who were hurt were the children of officers staying in nearby police lodgings, Idris Naim Sahin said.
The condition of the second police officer was unclear but Hurriyet newspaper said that he had been revived in hospital.
The interior minister described how the car had earlier sped through a police check point 90 km (55 miles) away in neighboring Kahramanmaras province, ignoring police calls to stop.
The attackers had driven into Pinarbasi after abandoning plans to strike another, unidentified target, reports said.
Television footage showed frantic scenes outside the police station, with fire engines and ambulances on site. Local media described an exchange of gunfire just before the bomb exploded.
“I heard a gun being fired and saw a policeman fall to the ground and suddenly there was an explosion. Shattered glass cut my hands, and I ran inside,” eyewitness Bahattin Ekinci said.
It is not clear if the device was detonated deliberately or as a result of the shooting.
Hasan Gumus, a civil servant who was working near the scene, said he and his colleagues had heard a “huge blast”.
“We saw a big cloud of smoke rising,” he told Reuters news agency.
Kayseri province is in the centre of Turkey, about 325 km from the capital, Ankara.
Nobody has so far said they carried out the bombing. But in an apparent reference to the separatist Kurdish PKK movement, Idris Naim Sahin said: “The crazy attacks of the terrorist organisation are continuing.”
Clashes between the PKK and the Turkish armed forces have increased in south-eastern Turkey over the past year, and the PKK has in the past carried out bombings in other parts of the country.
In September a powerful bomb in Ankara killed three people and wounded 15. That blast was blamed on the PKK.
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