The World Health Organization (WHO) said 44 cases of the disease have been reported in Tana River County in eastern Kenya, one of the areas hardest hit by widespread flooding.
"I believe that between government and national and international partners, we'll be able to contain it," the UN's resident coordinator in Kenya, Stephen Jackson, said in an interview with Citizen TV.
"We've contained cholera before, but it's a significant concern," he added.
Cholera is an acute intestinal infection that spreads through contaminated food and water and typically causes severe diarrhea, vomiting and muscle cramps.
It can be especially dangerous for young children.
"WHO will continue to support the health emergency response and remain vigilant for disease outbreaks that can easily spread if not quickly contained," Abdourahmane Diallo, WHO representative in Kenya, said in a statement issued by the UN's health agency on Tuesday.
"We must be agile and ready to respond, led by government and along with the partners, to bring relief to hundreds and thousands of affected people."
The flooding in Kenya has killed 238 people according to latest government figures published by the local media, while more than 200,000 have been made homeless.
Overall the heavier than usual seasonal rains, compounded by the El Nino weather phenomenon, have claimed the lives of more than 400 people in East Africa, a region highly vulnerable to climate change.