"Fears that the world's worst cholera outbreak could be set for a massive resurgence are growing," the relief organization said, AFP reported.
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.
Doctor Wadah al-Tiri said several patients had been transferred to Aden while others had been treated at a medical center in west.
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 four-year-long Saudi war on Yemen has killed tens of thousands of people and spawned what the United Nations calls the world’s most dire humanitarian crisis, with the country on the brink of famine.