"Probably at the end of August we will reach 300,000" cases, UN children's agency spokeswoman Meritxell Relano told reporters in Geneva during a conference call.
Since the outbreak was declared in April, an estimated 1,265 people have died, she said.
"The number of cases continue to increase," Relano said, adding that all of Yemen's 21 governorates have been affected.
She said that children had been hit hard by the outbreak, accounting for half of the registered cases to date.
But only a quarter of the people who have died so far were children, she said.
Cholera is a highly contagious bacterial infection spread through contaminated food or water.
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Although the disease is easily treatable, doing so in conflict-torn Yemen has proved particularly difficult.
Two years of war between the Huthi rebels and government forces backed by a Saudi-led Arab military coalition have killed more than 8,000 people and wounded 45,000 others.
According to the UN human rights agency, civilians account for nearly 5,000 of the recorded deaths and more than 8,500 of the injuries.
The conflict has also devastated the country's infrastructure, leaving more than half of its medical facilities out of service.
Yemen is also on the brink of famine, with about 17 million people -- two-thirds of the population -- uncertain of where their next meal will come from, according to the UN's World Food Programme.
"This is the largest humanitarian crisis happening in the world at the moment," WFP spokeswoman Bettina Luescher told reporters.
She said the agency was scaling up its response and aimed to provide food aid to 6.8 million people across the country this month alone.
But more than half of those people will receive reduced rations because of a dire funding shortage, she warned.