The UN agency said the disease had killed 2,971 people since August, including 198 in the past week, and infected 56,123 others.
In Zimbabwe, which has in recent years become a focus of international concern over widespread human rights violations, some 80% of people lack access to safe and clean water, the United Nations Children's Fund (UNICEF) earlier said.
UNICEF warned that the outbreak of cholera, which is spread by drinking contaminated water, could "get even worse due to a deteriorating sanitation system."
The extended economic crisis has devastated Zimbabwe's healthcare system, leaving the country, which recently introduced a 100 trillion Zimbabwe dollar bill worth about $300, virtually incapable of dealing with the cholera epidemic.
