"We are asking people to move to safer areas," a spokeswoman for the national relief agency said.
The south and centre have been placed on red alert because of the floods, which have claimed several lives.
In 2000, 700 people died and half a million were made homeless in Mozambique's worst flooding on record.
The worst affected areas are in the southern Gaza province, where a number of rivers are currently above crisis levels.
Emergency teams are on stand-by and motorboats have been dispatched to help transport people to safety, the AFP news agency reports. The evacuees will be brought to temporary shelters. Some of them have been set up in the capital, Maputo.
"We estimate there are 55,000 people affected," Rita Almeida from Mozambique's Disaster Relief Management Institute told AFP.
The town of Chokwe, home to a dyke, is particularly vulnerable, she added.
"We are registering very high water levels in the Limpopo and Inkomati rivers that could flood the town," Ms Almeida said.
From Sunday to Monday, almost 185mm (7 inches) of rain fell over the Limpopo basin, the AFP reports.
International observers have described the situation as critical. There are fears that the dyke in Chokwe could break, which would lead to chaos in the evacuations.
"If that dyke breaks, all those people will have to move more rapidly," the country chief of the World Food Programme, Lola Castro, said.
Neighbouring South Africa, Zimbabwe and Botswana have also been hit by severe flooding.
In South Africa, floodwaters claimed several lives and left hundreds stranded after the Limpopo river burst its banks on Monday.
Mozambique has started to evacuate some 55,000 people after heavy rains caused sea levels to rise to dangerous levels in parts of the country, officials say.