Tony Maryon, the head of the International Federation of Red Cross Societies (IFRC) team in Zimbabwe, said on Friday: "Because of the severity of this outbreak, we fear that it will take many more weeks to get it under control."
Aid agencies have been preparing for a worst-case scenario in which 60,000 people become infected with the water-borne disease, in part due to the rainy season and a weakened healthcare system.
The IFCR had launched an emergency appeal on December 23 for $9.2 million, but it is currently 60 per cent under-funded.
"As it stands now, we won't be able to continue our operations beyond the next four weeks," Maryon said.
The battle against the epidemic has also been hampered by a strike over pay by Zimbabwe's doctors and other municipal workers.
Cosmas Bundu, head of the municipal workers union, said: "We can't afford to continue to receive our salaries in Zimbabwe currency, which is not buying anything."
Last week, the country's central bank issued a 50 billion Zimbabwe dollar note. It is worth $1.25 on the black market.
Zimbabwe faces the world's highest official inflation rate. The municipal workers join teachers, doctors, nurses and even bus drivers in demanding to be paid in US dollars.