The governor of Aydin province told Turkish broadcaster CNN Turk that five others were injured in the tragedy on Friday, with one of them in critical condition.
Governor Huseyin Aksoy said initial testimonies from a restaurant worker suggested there was a leak in a cooking gas canister, leading to an explosion at around 3.35pm local time.
Reporters also said there was a fire following the explosion in the Turkish doner kebab shop in the Nazilli district of Aydin.
Footage showed fire trucks and ambulances at the scene, while smoke poured from the premises.
Photos showed windowpanes on all three floors of the building had been knocked out by the blast, while debris lay on the street outside.