The head of the rebel-installed Supreme Political Council, Saleh al-Samad, accused the envoy of bias and said he would no longer be allowed entry to rebel-held areas.
"We say unanimously that the envoy is no longer welcome here," Samad said in a televised speech late Monday.
"There will be no more contact with Ismail Ould Sheikh Ahmad and he is not welcome here."
Samad said the decision was taken jointly by the Huthi Shiite rebels and their allies in the General People's Congress of former president Ali Abdullah Saleh.
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He had been trying to broker a ceasefire for the holy Muslim fasting month of Ramadan which began on May 27.
More than 8,000 people have been killed since a Saudi-led coalition launched a military intervention in March 2015 to prop up the government of Abedrabbo Mansour Hadi.
Along with Sanaa, the rebels still control most of the north and the Red Sea coastline, including the key port of Hodeida.
With some 17 million people facing dire food shortages, UN officials have warned of the risk of famine.
The country has also been hit by a cholera outbreak that has killed more than 500 people.