They are all facing criminal negligence charges.
The prosecution requested arrest warrants for four additional crew members. Eleven others, including the captain, had been detained earlier.
Sewol ferry with 476 people on board sank off South Korea on April 16.
Divers have recovered 183 bodies, but scores are missing presumed drowned.
Many of the victims were students and teachers from Danwon high school, south of Seoul.
The ferry sank on a trip from the port of Incheon to the island of Jeju.
In the latest move on Saturday, the arrests warrants were issued for two helmsmen and two members of the steering crew.
Prosecutor Yang Jung-jin, of the joint investigation team, said the four crew members were taken into custody late on Friday, the Associated Press reported.
The 15 crew members are facing charges of criminal negligence and of failing to help passengers, the prosecution says.
On Friday, divers found 48 bodies of students wearing lifejackets in a single room on the vessel meant to accommodate just over 30 people.
The group was crammed into a dormitory and all were wearing lifejackets, a South Korean Navy officer said.
The presence of so many victims in the cabin suggested many had run into the room when the ship tilted, correspondents said.
The head of the operation to retrieve bodies said he had “no idea” how long the ship search would take.
The South Korean government has said it is “mobilizing all available resources” towards the rescue effort.
The prosecutors are also said to be investigating whether modifications made to the ferry made it more unstable.
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