Enforcement Directorate which investigates financial crimes in India had arrested Goyal late on Friday night.
Jet Airways did not immediately respond to a request for comment.
The case relates to an alleged 5.38 billion Indian rupees ($65.06 million) bank fraud case filed by state lender Canara Bank.
The bank had filed a complaint in May against the airline, Goyal, his wife and a former airline director for "causing wrongful loss" to the lender.
(Reporting by Jayshree P Upadhyay and Aditya Kalra; Editing by Tomasz Janowski)