Authorities believe improper stowage and overloading of cargo are one possible reason the ferry sank on April 16, leaving more than 300 people dead or missing.
Four employees at the ferry's owner Chonghaejin Marine Co who handled cargo on the Sewol, have already been arrested.
Kim Han-sik, president of Chonghaejin, was detained ahead of his possible formal arrest on allegations he was aware the ferry exceeded its cargo limit but did not do anything before it started its trip, according to senior prosecutor Yang Jung-jin.
Mr Kim, wearing a cap and mask, told reporters at a detention facility in the south port city of Mokpo: "I feel very sorry for the victims .... their family members. I committed a grave sin."
Mr Yang said prosecutors are investigating Mr Kim's actions before deciding if they will request a court to issue a warrant to formally arrest him.
All 15 surviving crew members involved in the ferry's navigation have been arrested, accused of negligence and failing to protect passengers.
More than three weeks after the sinking, 269 bodies have been retrieved but 35 others are still listed as missing. Searches have been hampered by strong currents.