The victim, named by Turkish diplomats as Eyup Orel, was working on a US-funded road project in eastern Kunar province when he was abducted on Tuesday.
President Hamid Karzai condemned the kidnappers, saying: "I am angered that the enemies of Afghanistan have killed a brother and fellow Muslim in pursuit of their goal of disrupting reconstruction in Afghanistan."
Orel was found dead on Wednesday morning after police closed in on the hostage-takers, interior ministry spokesman Lutfullah Mashal said. The driver and interpreter were freed earlier.
"After security forces cornered them they released the driver and interpreter but killed... the Turkish engineer," Mashal said. The kidnappers escaped after the shooting.
The engineer is the second Turk to die this year in Afghanistan. He is also the fourth foreigner to have been abducted in seven weeks, raising new fears of a wave of Iraq-style kidnappings in the war-torn country.
Orel had been in the country for less than two months and was working as a subcontractor for US firm Louis Berger on the Jalalabad to Asnar road, a company official said on condition of anonymity.
"His body is being transported by helicopter" from eastern Afghanistan to Kabul and will be handed over to Turkish military in the capital on Wednesday, he said, adding that the exact circumstances of his death remain unclear.
Afghan authorities had launched a major operation to find the hostage and secure his release, with security forces and local tribal elders sealing roads in and out of the province that borders Pakistan.
No group has come forward to take responsibility. But an Afghan official said earlier that militants linked to the Hezb-i-Islami group, led by fugitive former prime minister Gulbuddin Hekmatyar, were the prime suspects.
Insurgency-prone Kunar province is a stronghold of Hezb-i-Islami militants.
© 2004 Agence France-Presse