Fifty-nine people had died up until and including Thursday, and 617 others had been infected, bringing the total affected to 7,359, the ministry added.
The news came as the local authorities and relief agencies attempted to get clean drinking water to those areas worse affected by Hurricane Tomas.
The storm caused flooding and left eight people dead in western Haiti.
The charity, Save the Children, said that in Leogane, the streets had been turned into "rivers" and some 35,000 people had been affected.
The BBC's Laura Trevelyan in the town said the water reached her knees, and that people were afraid of the risk of disease.
There was also flooding in Les Cayes, Jacmel and Gonaives, while many mountain towns have been cut off by flooded roads and landslides.
There was widespread relief on Friday after Hurricane Tomas passed without destroying the tented camps in and around the capital, Port-au-Prince, housing about 1.3 million survivors of January's earthquake.
However, attention soon turned to preventing the spread of cholera, which is caused by bacteria transmitted through contaminated water or food, in the unsanitary conditions.
Cholera causes diarrhoea and vomiting, leading to severe dehydration, but can kill quickly. It is treated easily through rehydration and antibiotics.
A spokesman for the Pan-American Health Organisation, Christian Lindmeier, told the Reuters news agency: "Cholera is a water-borne disease and so additional water means additional risk."
"We do expect the infection rate to jump up due to the flooding and to the bad sanitation conditions in many areas," he said.
In the town of Saint Marc, in the northern region where the outbreak began three weeks ago, a Cuban doctor in charge of the local hospital said there had been more cases of cholera since the hurricane.
"The situation here - after the storm - has worsened," Dr Buenaventura Sanchez told the Associated Press.
"We are seeing higher numbers [of cases] than in the days before, and we are also seeing cases of cholera with typhoid fever at the same time."
Like cholera, typhoid is caught by consuming contaminated food or drink that has been handled by an infected person, or if contaminated sewage gets into water used for drinking or washing food. It can also be fatal if not treated.
Gary Shaye, the country director of Save the Children, said thousands of children in Leogane were now at increased risk of diarrhoeal diseases.
On Friday, Haiti's government and the United Nations appealed to donors for nearly $19m to cover urgent humanitarian needs.