Portuguese Prime Minister Luís Montenegro will temporarily take over her role, the statement said.
An ongoing series of deadly winter storms have wreaked havoc on the European Union nation of 10.7 million people, triggering floods, landslides and power outages, and causing significant infrastructure damage across many parts of the country.
Amaral, a lawyer, was criticized for her government's slow response, particularly during Storm Kristin, which struck the country in late January, killing six people, according to media reports.
Another person died last week when Storm Leonardo hit Spain and Portugal.
Amaral is the first minister to step down since the center-right government led by Montenegro came to power last May.