Those living close to the Uruguay River in Entre Rios province are reported to be among the worst affected.
The mayor of the town of Concordia, on the border with Uruguay, was quoted as saying a quarter of the town was underwater.
Thousands of people have also been affected by the rains in neighbouring Paraguay and Uruguay.
"There's never been flooding like this," Concordia Mayor Enrique Cresto said on Thursday, according to the Clarin newspaper.
"Today the river is going to rise another 40cm [16in]. We are going to... keep evacuating more families all day."
The provinces of Formosa, Chaco and Santa Fe are also reported to be badly affected.
Chaco government general secretary Horacio Rey said a "comprehensive assistance plan for those affected" was being implemented.
It would include "sanitary operations, delivery of merchandise, assistance to producers and infrastructure projects to protect against the costs", Mr Rey told the state-run Telam news agency.
The floods have been linked by some experts to the El Nino phenomenon, a naturally occurring weather episode that sees the warm waters of the central Pacific expand eastwards towards North and South America.
What is El Nino?
Current El Nino 'among the strongest'
At least 7,000 people have been evacuated in north-eastern Argentina as heavy rains cause rivers to swell.