"We estimate that there are ten million people affected by floods in July, and 10 million by the most recent floods," said Winnie Romeril, a spokeswoman for the International Federation of Red Cross and Red Crescent Societies.
"A lot of people were displaced twice," she told AFP.
The international aid appeal will focus on providing a month's food supplies for nearly 200,000 people in the hardest hit regions, the federation said in a statement.
The number affected covers those displaced or whose homes were either destroyed or damaged after floods and Typhoon Lekima hit Vietnam last week, Romeril said.
Vietnamese officials have described the floods as the worst in 45 years in some regions.
Authorities said the floods have either destroyed or damaged more than 134,400 houses and inundated more than 160,000 hectares (400,000 acres) of rice fields and other crops.
"It's really two emergencies with the same result," Federation staffer Joe Lowry said in the statement.
"The mountainous regions are facing killer flash floods while in the lowlands, standing water simply refuses to drain," he added.
Six of the worst affected provinces were already under water following three days of rainfall before the typhoon struck, according to the Red Cross.
Damaged dams and swollen rivers flooded communities, washed away homes, roads and bridges and forced the evacuation of hundreds of thousands, it added.