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Goldberg said Walters, 83, who is in a New York hospital, has been told to rest and is not receiving visitors.
"You all know that she fell and cut her head 10 days ago and then was running a temperature," Goldberg said on the show.
"But it turns out it is all the result of a delayed childhood. Barbara has the chicken pox," Goldberg adding, saying Walters had never had the illness as a child.
Walters, 83, had been admitted to a Washington hospital during President Barack Obama's inauguration weekend after she fell and cut her head at the British ambassador's residence, her network ABC said.
Goldberg joked: "She's been told to rest, she's not allowed any visitors, and we're telling you, Barbara, no scratching."
ABC-TV said Walters, who created the long-running talk show after working decades as one of television news' best-known journalists, was transferred to a New York hospital late last week from Washington and was expected to be discharged soon.
Despite Goldberg's light-hearted remarks about the illness, usually associated with children, chicken pox can be serious for adults and the elderly, accompanied by more severe itching from hundreds of blisters.
Headaches, fever and chills, sometimes leading to pneumonia, can follow if the illness is not properly treated and precautions are not taken, or if the patient has a compromised immune system.