Lee Joon-Seok faces five charges, including negligence of duty and violation of maritime law, the agency said.
A joint investigation team of police and prosecutors on Friday had sought arrest warrants for Lee, 52, and two of his crew without specifying charges, the coastguard had said.
Yonhap on Saturday said a local court in Mokpo had issued warrants for him and two other crew members, citing the possibility that they may flee or destroy evidence.
Earlier, prosecutors said Lee had handed the helm to his third officer before the ferry capsized.