Hundreds of police and emergency workers have been put into the rescue operation.
Several localities along the Danube took urgent measures to stop the "blue river" overflowing.
"The situation is tragic, the damage is of a scale hard to imagine," Gheorghe Flutur, president of Suceava department, one of the worst hit regions, told Mediafax news agency.
Twenty-one dead have been confirmed and at least one person was missing since the floods started last week, emergency inspectorate spokesman Alin Maghiar said.
"Most of the people died after being carried away by high waters. One fell from his house and two others were killed by lightning," he added.
Most of the deaths occurred on Monday night in two departments close from the Ukrainian border.
In the northeastern town of Dorohoi, six people died in the night of Monday to Tuesday, according to officials. More than 1,700 people had to be evacuated and some scrambled up trees to get away from the rising waters, according to witnesses.
The water receded on Tuesday afternoon but houses were badly damaged by floods which rose above one metre (3.3 feet) in some places. Roads into Dorohoi remained under water.
Heavy rain has been falling for much of the past week in the Balkan country and forecasters have warned that it will continue in northeast Romania until Wednesday morning.
Several old people had died last week in the central regions of Romania after being carried away by high waters.
In the northern Suceava department, hundreds of people were evacuated on Tuesday afternoon as the river Siret threatened to overflow.
"Ten villages have been evacuated. 1,870 people will spend the night in monastries, schools, cultural centres or with relatives", a spokeswoman for the Suceava local authorities told AFP.
Some 1,100 sheep were moved to higher ground in the mainly rural region.
Further along the Siret river, in Sendreni, inhabitants and emergency servicemen reinforced dykes with bags of sand to prevent floods.
Prime minister Emil Boc flew to the affected zones in northeastern Romania. He said Bucharest could ask help from an emergency European funds once the scale of damage has been clearly established.