Kwon Yun-Ja, 72, was arrested at a flat in the southern suburbs of Seoul following a successful ambush, Yonhap news agency said.
Authorities believe the businessman, Yoo Byung-eun, owns the ship and that his alleged corruption may have contributed to the sinking.
As the crew members stood with bowed heads, families of the victims struggled to contain their fury.
Prosecutors asked for a court-issued arrest warrant after billionaire businessman Yoo Byung-Eun failed to heed an official summons.
15 crew members involved in the ferry’s navigation have been arrested, accused of negligence and failing to protect passengers.
South Korean recovery workers strengthened a ring of netting around a sunken ferry to try to prevent corpses drifting away.
S. Korean President Park Geun met families of ferry victims for the second time as divers recovered two more bodies
The operation to recover bodies from the ferry that sank off South Korea last month has been suspended due to heavy seas.
Divers have recovered 212 bodies from the wreckage, but 90 passengers are still missing.
The apology came as divers on Tuesday fought strong currents in their search for more than 100 missing passengers.
Prosecutor Yang Jung-jin of the joint investigation team says two helmsmen and two members of the steering crew were detained Saturday.
Officials said on Tuesday that confirmed fatalities had reached 104, with nearly 200 people still missing.
The S Korean President said that “legally and ethically, this is an unimaginable act.”
At least 23 of the dead are students, according to coast guard spokesman Kim Jae-in. Divers have yet to find any survivors in the ship.
Divers recovered 13 bodies from inside a ferry that sank off South Korea, pushing the confirmed death toll to 46, officials said.