They set off the car bomb they had prepared, the official Anadolu news agency said, adding that the two suspects were dead.
There were no immediate reports of any other casualties in the blast, which occurred Saturday morning in the outskirts of the city.
Ankara governor Ercan Topaca told reporters at the scene it was “likely” that they had connections to the outlawed Kurdistan Workers’ Party (PKK).
“The materials used, the construction and the way it was planned point to the PKK a little,” he said, quoted by Anadolu.
Violence returned to the region after the collapse of a two-year ceasefire last year.
The governor said police began an operation early on Saturday to find the suspects after a tip-off came from Diyarbakir, a mainly Kurdish province in Turkey’s southeast.
In televised comments, Topaca also said the suspects were a male born in the eastern province of Bingol and an unidentified female. She was later named in Turkish media.
He added that the authorities were looking for a third person and that “interestingly” the suicide bombers hung a Turkish flag on the car.
CNN-Turk broadcaster reported that 200 kilos (more than 400 pounds) of ammonium nitrate and plastic explosives were seized during the operation.
The bombing comes two days before the first anniversary of Turkey’s deadliest terror attack in its modern history in Ankara which left 103 dead.
And on Friday, the Kurdish group Kurdistan Freedom Falcons (TAK) with ties to the PKK claimed responsibility for a motorbike bombing on Thursday near a police station which wounded 10 people. -AFP