A spokesman for the prosecutor and police investigation announced the arrest warrants Friday.
According to state prosecutor Jae-Eok Park, "It is not clear where (the captain) was when the accident occurred, although it is clear that he was not in the steering room before the actual accident happened."
Captain Lee Joon Suk offered a televised apology on Thursday.
The cause of the accident, which left 28 dead and 270 still missing, has not yet been determined. A search and rescue operation is ongoing as divers try to reach passengers they believe may still be on the ship.