The rumors, which appeared on social media Tuesday, caused the Sacombank stock (STB) to fall by 5.7% in the morning before closing the day 4% lower at VND30,200 (US$1.22).
The government usually imposes such a ban to investigate someone for possible crimes.
But ministry spokesperson To An Xo dismissed the rumors saying Minh is not even on a watchlist.
"The Ministry of Public Security refutes all false information that is spread to cause negative impacts on the financial and banking system. Those who spread false rumors will be punished."
Sacombank also denied the rumor on Tuesday, and assured its customers that all operations continued as usual.
Minh, 64, has been chairman at several companies including LPBank, and took over at Sacombank in 2017.