It said that one died in the explosion and the other was "neutralized" by authorities there.
A recording of CCTV footage showed a person getting out of a vehicle and running towards the government building, followed by clouds of smoke from an explosion.
A senior Turkish official told Reuters the attackers had hijacked the vehicle and killed its driver in Kayseri, a city 161 miles southeast of Ankara, before carrying out the attack.
Two police officers were also wounded in the incident.
Police announced they would also be carrying out controlled explosions for "suspicious package incidents" in other parts of Ankara.
Authorities did not identify any specific militant group.
The blast on Ataturk Boulevard was the first in Ankara since 2016, when a bomb-laden car exploded at a crowded central transport hub killing 37 people.
During a spate of violence in 2015 and 2016, Kurdish militants, Islamic State and other groups either claimed or were blamed for several attacks in major Turkish cities.
The incident also comes on the day that Turkey's parliament was set to open a new session.
Ankara's chief prosecutor has launched an investigation into Sunday's incident.
