Yonhap says 68-year-old Lee Joon-seok was detained early Saturday.
The ship, the Sewol, sank Wednesday, leaving hundreds missing and feared dead.
The investigation into the disaster has focused on the ferry's sharp turn before it started listing, and on whether a quicker evacuation order by the captain could have saved lives. Investigators also were determining whether the captain had abandoned the ship.
Rescuers are searching for about 270 people still missing and feared dead.
At least 28 bodies have been recovered. Officials said there were 179 survivors and about 270 people remain missing, many of them high school students.
Yonhap said two crewmembers were also arrested.