This came as the World Health Organisation said on Monday it was investigating the possibility that two of the siblings passed the disease to each other.
Vietnamese officials, however, said there was no evidence of human-to-human transmission in the cases.
Nine people have died of bird flu in Vietnam in the past three weeks.
The 36-year-old man from Thai Binh province tested positive for the H5N1 strain of bird flu, the Pioneer newspaper quoted Vice-Minister of Health Tran Chi Liem as saying.
His 47-year-old brother died on 10 January from bird flu, while another brother, 42, was recovering in a hospital in Hanoi after also testing positive for the virus.
Health officials have said the family had eaten raw duck blood pudding in late December, linking their infections to poultry.
Nine Vietnamese have died of
bird flu in the past three weeks
"From the H5N1 virus-infected cases in Thai Binh recently, there is no evidence of human-to-human transmission," Liem was quoted as saying.
However, the WHO has not ruled out the possibility of person-to-person transmission because the middle brother cared for the elder sibling before he died. The WHO has not confirmed reports of the third brother's infection.
But that alone would not raise the threat of a flu pandemic, said Peter Cordingley, spokesman for the WHO's Western Pacific regional office in Manila.
Similar isolated cases of possible human-to-human transmission occurred in Hong Kong in 1997 and in Vietnam and Thailand last year, he said.
Last year the virus surfaced in 10 Asian countries, killing or forcing the slaughter of more than 100 million birds.
The virus was passed on to humans in Vietnam and Thailand, killing 29 and 12 people respectively.