"Fears that the world's worst cholera outbreak could be set for a massive resurgence are growing," the relief organisation said on Thursday.
It said aid agencies were struggling to reach suspected cases.
In a statement, Oxfam pointed to "fighting and restraints on access, including checkpoints and permit requirements imposed by the warring parties", and warned the coming rainy season was likely to accelerate the spread of the disease.
The water-borne bacterial infection has claimed more than 3,000 lives in Yemen since the outbreak began in 2016, according to Oxfam.
At a medical centre for the displaced in the government-held western town of Khokha, Qassem Suleiman had brought his son Alaa for tests after a serious case of diarrhoea.
War leaves 16 million Yemenis without clean water: Oxfam
Doctor Wadah al-Tiri told AFP that several patients had been transferred to Aden while others had been treated at the Khokha centre.
He said a tent was to be set up for suspected cases.
The doctor said Yemen badly needed international aid to combat the epidemic.
The UN's humanitarian coordination office OCHA said last month that children under the age of five make up nearly a third of this year's cases.
The spike, which comes two years after Yemen suffered its worst cholera outbreak, was concentrated in six governorates including in the Red Sea port of Hodeida and Sanaa province, both combat zones, it said.
The war in Yemen
Yemen's conflict, which pits Iran-linked rebels against a regional pro-government alliance led by Saudi Arabia, has left some 10,000 people dead since 2015 and pushed millions to the brink of famine.
Aid groups say the actual death toll could be five times as high.
The war has created the perfect environment for cholera to thrive, as civilians across the country lack access to clean water and health care.
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