By Agence France-Presse
Tran Phuong Binh, his deputy Nguyen Thi Ngoc Van and three others were arrested for "violating laws on financial and banking activities", according to a statement from the partially state-owned Dong A Bank on Saturday.
The statement did not elaborate on what crimes the five are accused of, but state-run Thanh Nien newspaper said Binh is suspected of causing major financial losses as a result of poorly managed loans.
All five were originally dismissed in August 2015, Dong A Bank's statement added, when the bank was put under special supervision for suspected illegal activities, according to reports.
Dong A Bank, one of the country's smaller banks and based in Vietnam's financial hub Ho Chi Minh City, was established in 1992 and lists the city's communist party office as one of its major shareholders.
Vietnam has shown strong economic performance in recent years, with GDP growth hitting 6.4 in the third quarter of this year.
But soaring debts have contributed to slowing growth.
The communist government has vowed to clean up the country's troubled banking sector, hampered by a series of scandals in recent years, including dodgy lending and embezzlement, which have led to several high-profile arrests.
In September this year, 36 former bank employees from Vietnam Construction Bank, including the chairman, were convicted for stealing more than $400 million, reportedly the largest sum ever pilfered from a bank in Vietnam.