The militants, believed to be female and a male, were suspected of planning to execute the state, a car bomb attack -run Anadolu news agency reports.
After they were asked to surrender their weapons the devices detonated.
Police had been acting on a tip off, Ankara’s governor said, suggesting a link to Kurdish separatists.
Erkan Topaca said authorities had discovered the pair hiding at a horse farm in the district of Haymana, only outside the capital.
He said: “The organisation they can be associated to is not clear yet but according to information we’ve received it’s highly likely that [the guy] is linked to the PKK (Kurdistan Workers Party).”
The BBC’s Mark Lowen in Ankara says the pair were said to be flying a Turkish flag as cover and a third person is now being sought.
Ammonium nitrate and plastic explosives were discovered with the vehicle.
Kurdish militants have carried out a wave of bombings across Turkey since a ceasefire broke down in 2015.
The Turkish president has vowed that the PKK, which has waged a four-decades-long fight in Turkey, will be “annihilated”.
But, our correspondent says, with the strikes continuing and deepening between Kurds and the Turkish state, there is little hint of the finishing that is insurgency and neither side has shown a readiness to return to peace negotiations.