The blast occurred late on Saturday near the airport of Van in southeastern Turkey, which has a mainly ethnic Kurdish population.
The motive for the attack was not immediately clear but a local official said he suspected the separatist Kurdistan Workers Party (PKK), though nobody had claimed responsibility.
A local newscast quoted Van Governor Hikmet Tan as saying the attackers may have been targeting him because he had been due to pass by the area a few hours later on his way to meet Prime Minister Tayyip Erdogan in a nearby town.
“There is a strong possibility that the terrorists are members of the PKK,” Tan was quoted as saying by the Anatolian news agency.
The injured man hid for eight hours after the explosion in a sentry post, bargaining with police in the Kurdish language before giving himself up.
The identity of the two bombers was not immediately clear, but the PKK has recently launched a number of attacks on security forces in eastern Turkey after ending a six-year unilateral ceasefire.
More than 30,000 people have died in southeastern Turkey since 1984 when the PKK began its violent campaign to create an independent homeland in the impoverished region.
The violence fell sharply after PKK leader Abdullah Ocalan was captured in 1999.
Turkey has recently enacted more cultural rights for its large ethnic Kurdish minority as part of its drive to join the European Union.