"Aid is more necessary than ever. This is a critical moment."
The UN has appealed to donors to provide $567m of aid to Zimbabwe, where about 5.5 million people are suffering from a shortage of food amid the world's highest rate of inflation.
But no country has yet contributed to the appeal, Byrs said.
Zimbabweans are now allowed to use foreign currencies in the country as part of an attempt to head off hyperinflation.
Civil servants in health facilities and schools are now being paid in US dollars after many of them refused to work for Zimbabwean currency, Byrs said.
The cholera epidemic also comes amid a political stalemate that has dragged on for months and crippled the government.
The dispute over forming a unity government now seems close to being resolved, with the opposition Movement for Democratic Change (MDC) agreeing to join the government led by Robert Mugabe, the Zimbabwean president.
Nelson Chamisa, a spokesman for the MDC, told Al Jazeera that a resolution of the political dispute would pave the way to solving the cholera crisis.
"The solution has to do with the capacity of government to respond to the challenges and also to put in place preventative mechanisms," he said.
"I have no doubt that with a willing and competent government it will be very easy to deal with these challenges."
The epidemic shows no sign of stopping, with 1,493 new cases including 69 deaths reported in the past 24 hours, according to the UN.
Two of out of every three deaths are being recorded outside of the cholera treatment centres, Byrs said.