The branch will have a registered capital of US$15 million, the central bank said in a statement on its website.
SMBC opened its first branch in Ho Chi Minh City in December 2005, also with a registered capital of $15 million.
Standard Chartered, HSBC Holdings and Australia and New Zealand Banking Group (ANZ) this year received approval from the Vietnamese government to run fully foreign-owned units.
A total of 29 overseas banks have branches and another 38 foreign lenders have opened offices in Vietnam, according to the central bank’s website.