The Dogan news agency said Ramazan Dogru, general manager of the mine owned by Soma Holding, and its operations manager Akin Celik were among those detained.
Prosecutors said three people were held on charges of negligence and were also accused of the crime of causing the death of more than one person, a charge that does not imply intent.
The charges can lead to sentences of between three and 15 years in prison, according to the Turkish penal code.
Government and company officials have insisted that the mine was inspected regularly and negligence was not a factor.
But there has been widespread public anger. Police used water cannon to disperse rock-throwing protesters in Soma, where about 1,500 demonstrators urged Prime Minister Recep Tayyip Erdogan’s government to resign.
In Istanbul, police forcefully broke up a crowd of about 150 people who lit candles and lined up mining helmets on the ground to honour the victims.
Reacting to the unrest, government officials have promised to investigate and pledged that any mine officials found to be negligent would be prosecuted.
The Milliyet newspaper said on Saturday that a preliminary report by a mine safety expert who inspected the Soma mine suggested that smouldering coal caused the mine’s roof to collapse.
The report said support beams were made of wood, not metal, and the mine had too few carbon monoxide sensors. Company officials insist safety standards were high, noting that the mine contained 50 gas sensors and employees were given gas masks.
At a Press conference on Friday, Mr Celik said thick smoke from the underground fire killed many miners who were not carrying gas masks.
Rescue workers entering the mine complained of high levels of carbon dioxide and carbon monoxide.
On Saturday, rescue workers retrieved the bodies of the last two miners missing in the disaster and completed their search.
Energy minister Taner Yildiz said it brought the death toll from the disaster to 301. Another 485 miners escaped or were rescued.
“All corners of the mine were searched by a large team and there was no other body or living person,” he said.
“Until today we had focused on search and rescue efforts. Now we will be focusing on investigations, on what will happen about production.
“We won’t be leaving (Soma) because the search efforts are ending,” he added. “There will be psychological and social support.”
But one miner, 24-year-old Erdal Bicak, claimed the disaster was due to negligence by the mining company.
“The company is guilty,” he said, adding that managers had machines that measure methane gas levels. “The new gas levels had got too high and they didn’t tell us in time.”