The fire swept through the secondary school dorm in Aladag in Adana province and authorities said it may have been caused by an electrical fault.
However, there were fears that the girls may have been unable to escape. The mayor said it was likely that a fire door had been locked.
The girls who died were aged 11 to 14.
The dormitory housed girls from impoverished families in nearby villages, reports said.
One of the girls who died was Zeliha Avci, 13. Her father was waiting on Wednesday for the authorities to allow him to collect her body for burial in her village.
"No-one has called me," Mustafa Avci complained. "We learned about the fire from the news and ran to the scene. Our children have been burnt to death and no-one gives us any information."
Mr Avci last saw his daughter at the weekend. "She was very keen to go to school and get educated, but her days are over now," he said.
Her old dorm, he explained, was torn down in 2015 and he was unhappy about the new one. "This was the only dorm in town. We didn't want to send her there, but we had no other option."
TV footage showed flames leaping from the roof of the building as firefighters battled to put it out.
Adana governor Mahmut Demirtas said some students had been injured when they jumped from windows to escape the fire. He said 34 students had been staying in the dorm and 22 were taken to hospital.
A government minister who visited the scene said claims that the fire exit had been locked would be investigated. Turkish authorities imposed a media blackout on local coverage of the disaster.
Anadolu news agency said the six people in custody included the head of the dormitory, three teachers and two other staff. They were being investigated on suspicion of causing death by negligence.
A dormitory manager and five others have been detained in southern Turkey after a fire claimed the lives of 11 schoolgirls and a teacher, reports say.