Bulent Gulbay, 39, hung himself in his cell in a jail in the central province of Karaman, where he was moved from another prison after being attacked by fellow inmates, the agency said.
The man was sentenced to life in 2006 for raping and strangling to death Lisa Eder, who was holidaying with her family in Alanya, a Mediterranean resort popular with German tourists.
Gulbay, who had twice been convicted for molesting minors in the past, had been running a souvenir shop near the hotel where the Eders were staying in October 2004.
The girl's body was found dumped in the ruins of a castle outside Alanya a day after she went missing after visiting Gulbay's shop.
The murder sparked a huge uproar in Alanya, prompting the city council to ban ex-convicts from running shops in the area, which is home to some of Turkey's largest tourist resorts.