Hillary, 87, returned to Wellington Sunday after a trip to the Kathmandu, Nepal, and apparently then had a fall, the New Zealand Herald reported.
His wife and children refused to comment on what Hillary's condition was, the newspaper said.
Tuesday night, New Zealand Prime Minister Helen Clark sent out a national "get well" message on Radio New Zealand.
"There's no one we love more," Clark said. "I think the message from every single one of us is 'hang in there Sir Ed, we love you.'"
Hillary and Tenzing reached the peak of Everest on May 29, 1953. Tenzing died in 1986.