The 35-year-old prosecutor died in the intensive care unit of the Fırat University Hospital on Thursday, officials said.
Uzun was shot in the head by an unidentified assailant in the Ovacık district while he was returning to his apartment on Wednesday. He was rushed to the Ovacık State Hospital for urgent treatment and then taken to the Fırat University Hospital.
A police operation has been launched to capture the assailant, who fled in a car immediately following the incident.
Four people have so far been detained on suspicion of links to the armed attack, security forces said.
In February, Doğubayazıt Public Prosecutor Hakan Kılıç was shot dead by an unidentified individual in the eastern province of Ağrı.