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.

But what will this mean for consumers - particularly those who are suffering from slow broadband - or none at all?
Rival telecoms companies have long argued that Openreach - the firm providing most of the UK's broadband infrastructure - should not be part of the same group as BT, which has a third of the country's broadband market.
The likes of Sky and TalkTalk say this structure has been bad for competition and consumers.
Ofcom agreed - as did the Department for Culture, Media and Sport. To avoid a protracted legal battle, BT has now fallen into line.
The jury is still out. BT will still control Openreach's budget, even though the newly separated company will have its own boss and decide how to spend its cash.
Really fast broadband requires running fibre optic cable into every home, which is very expensive. As a result, most UK broadband connections still rely on the elderly copper wires used for telephone calls.
Andrew Ferguson, of the news website ThinkBroadband, said it is unclear whether separating BT and Openreach will deliver this faster option.
Most observers agree that the split alone will not solve the UK's broadband problems.
Slow and non-existent broadband is still an issue in some rural areas and Openreach has been criticised for its failure to address the issue. However, very few other operators appear willing to fix the problem, which is expensive and technically challenging.
You have a broadband fault but it is taking weeks to fix. Sound familiar?
Critics say Openreach just failed to provide adequate levels of customer service because complaints come through a customer's internet service provider, giving it no incentive to undertake repairs more quickly.
Gavin Patterson, BT chief executive, admitted on Friday that Openreach's service has "not been where it needed to be" and said the separation would improve the situation.
It remains to be seen how long that will take to deliver - and to remove the BT logo from thousands of BT white vans.
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.
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Ofcom, the telecoms regulator, said on Friday that BT had agreed to "legally separate" Openreach - the division that owns and operates the UK's broadband network.