The dead were aged 25-43 and the injured woman was 22 years old.
All four persons were cleaning up after a downpour when a house wall collapsed on them, the Giao Thong newspaper reported.
Authorities are searching through the rubble to find out if there are more victims and to try and find out why the accident happened.
The latest reported deaths take the death toll of heavy rains in northern Vietnam to six. Landslides and floods triggered by the heavy rains had killed three people in the provinces of Tuyen Quang and Hoa Binh, while destroying 260 houses.
A low-pressure area over the northern region had triggered rains starting May 19, but the heaviest ones showed up since last Saturday.
Floodwaters have damaged 9,500 hectares of rice fields in several localities, with Hanoi suffering the most, losing more than 4,000 hectares, followed by Tuyen Quang and Phu Tho with 1,500 hectares each.
Between 7 a.m. and 3 p.m. Tuesday, rainfall was measured at almost 200 mm in Thai Binh, more than 130 mm in Hai Phong City, 80 mm in Tuyen Quang, and almost 90 mm in Bac Ninh and 70 mm in Thai Nguyen.
The rains began to subside Wednesday in northern and central Vietnam, though mountainous areas in the north may see rains continue for a few days more, meteorologists said.