Hospitals in the city, which is controlled by Houthi rebels, are crowded with cholera patients.
Dominik Stillhart, ICRC director of operations, tells a news conference in Sanaa that hospitals are struggling with an influx of patients from a cholera outbreak.
It said that there were 2,752 suspected cholera cases and 58 more people have been confirmed as having the diarrheal disease.
Yemen has fallen into civil war in 2014 after Houthi rebels overran Sanaa and other provinces.
Only a few medical facilities are still functioning and two-thirds of the population are without access to safe drinking water, the United Nations has said.
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According to World Health Organization figures, about 7.6 million Yemenis live in regions with high risk of transmission of this bacterial disease that is transmitted by ingestion of contaminated food or water. Death can also occur within hours if a patient is left untreated. It is the second outbreak in less than a year of the bacterial infection carried by contaminated food or water which causes diarrhoea and dehydration.
Nearly 300 hospitals or clinics have been damaged or destroyed in fighting between forces loyal to President Abdrabbuh Mansour Hadi - who is backed by a Saudi-led multinational coalition - and those allied to the Houthi rebel movement.
Sanaa has been worst hit, followed by the surrounding province of Amanat al-Semah, the World Health Organisation (WHO) says.
Dr. Nevio Zagaria, WHO representative in Yemen, said in a statement, "We are very concerned with the re-emergence of cholera across several areas of Yemen in the past couple of weeks".
More than 8,000 people have been killed since the Saudi-led Arab coalition intervened to support Yemen's government in 2015, according to the WHO. The health system, severely degraded by more than two years of war that also displaced millions, can not cope, the state news agency, Saba, said.
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