The original report had also been carried on the government's official website.
Vietnam News Agency said in a statement that it had apologised to Phung Dinh Thuc and Do Van Hau over the false report. It also apologised to their families and to police.
The news agency said it had failed to verify its information "carefully enough" before publication.
Former PetroVietnam chairman Dinh La Thang, 56, was arrested on Friday. The former member of Vietnam’s politburo is the most senior executive arrested so far.
Thang’s brother, Dinh Manh Thang, former chairman of a PetroVietnam unit, was also arrested on allegations of violating state regulations on economic management.
Government critics have voiced suspicions that the corruption crackdown is politically motivated, at least in part, and aimed against those close to former Prime Minister Nguyen Tan Dung, who lost out in an internal power struggle in 2016.
The corruption crackdown made global headlines in August when Germany accused Vietnam of kidnapping former executive Trinh Xuan Thanh in Berlin to face trial over a separate case.