The units were made in Thailand between Feb. 7 and May 15 last year, according to Vietnam Register.
A representative of Triumph Vietnam said the kickstand of affected bikes had been manufactured with the use of an incorrect specification of raw material that causes it to bend over time.
This could result in the bike falling over if parked for extended periods.
Dealerships in Vietnam will replace the faulty component without any charge between May 30, 2022 and May 25, 2024.
Triumph Trident 660 was launched in Vietnam in early April, with a price tag of VND270 million ($11,640).