DNA testing revealed the fraternal twins, who are now two years old and look "strikingly different", had been conceived from the sperm of two different men.
Twins can have different fathers if two eggs from the same mother are fertilised by sperm from two different men (picture posed by models)
The Vietnamese mother and her husband had taken the twins for DNA testing after suspicions over the children's parentage were raised by the man's family because one has thick, wavy hair, the other twin has thin, straight hair.
They were shocked to learn only one of the twins was biologically related to the husband, but both were related to the woman - ruling out any possibility that one of the twins could have been swapped at the hospital shortly after birth- according to reports from the state-run Tuoi Tre newspaper.
Le Dinh Luong, president of the Genetic Association of Vietnam, told AFP news agency it was an extremely rare case.
"Our Centre for Genetic Analysis and Technology lab has tested and found a pair of bi-paternal twins," he said.
"This is rare not only for Vietnam, but for the world."
The occurrence, known as heteropaternal superfecundation happens when a woman ovulates two eggs during one cycle, which are then fertilised by two men within a period of about five days.
In May 2015 an American judge ruled a woman's former lover only had to pay half of his child support - because one of his twins had a different father.
The case began in October 2014, when social services filed a child support request on the mother's behalf, naming the man as father of both girls.
A DNA test was later ordered, which showed only one of the babies was related to the man, prompting the mother to admit to the court she had been intimate with another man in the same week the babies were conceived.
Judge Mohammad's ruling set a precedent as no known case like this had ever been seen before.