"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.

The Leinster full-back damaged his bicep towards the end of Saturday's 63-10 win over Italy in Rome.
The Irish Independent has reported that the injury could require surgery and Kearney is set to miss this week's three-day training camp in Monaghan.
Ireland have declined to comment on the extent of the injury but will issue an update on the situation on Friday.
The 30-year-old is in a race to be fit for the matches against France, Wales and England.
Simon Zebo is the most likely candidate to assume the number 15 jersey should Kearney be missing, with Ulster's fit-again Andrew Trimble coming on to the wing.
Robbie Henshaw is set to train this week despite suffering a dead leg.
The centre was forced to retire hurt with the injury against the Italians but is likely to join the Irish squad when they get together on Wednesday.
Flanker Peter O'Mahony, who was not considered for Ireland's opening two Six Nations games because of a hamstring injury, trained with Munster on Monday, but will not play for the province against the Ospreys on Saturday.
Meanwhile, Jamie Heaslip has agreed a new contract with the Irish Rugby Football Union, which will see him continue to play for Leinster and Ireland until the end of the 2019 Rugby World Cup in Japan.
The 33-year-old number eight has won 93 caps for Ireland, scoring 13 tries and has started 36 of Ireland's last 41 Test matches.
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.
[NEXT_CONCEPT]
Rob Kearney could be ruled out of the remainder of Ireland's Six Nations campaign with an arm injury.