Winfrey told the Entertainment Tonight programme on CBS an assistant in a luxury boutique had refused to show her a black "lizard or alligator skin" handbag she had asked to see.
"We are fuming – this person acted terribly wrong. We are sorry this happened to Oprah," Switzerland Tourism said in a Tweet.
Spokeswoman Daniela Bär told the Blick newspaper the incident was damaging for Switzerland's image but was a one-off that wouldn't have a lasting impact on the country's popularity with tourists.
However, she called on the store owner to make a full apology.
Winfrey said the store assistant had told her the bag would be too expensive for her and offered to show her others instead.
The celebrity is one of the wealthiest women in the world with a fortune estimated at 2.5 billion dollars.
Having been refused the bag, Winfrey says she left the shop without buying anything.
She said she rarely experienced racism – possibly because she was so well known.
Blick said the incident occurred in the chic Trois Pommes store whose owner Trudie Götz was also a guest at Turner’s wedding.
She apologized for her assistant’s behaviour, saying there had been “a misunderstanding between her and Oprah”.
The bag cost 35,000 francs and was placed behind a security panel, the paper said.
“We don’t have any facial recognition here,” Blick quoted Götz as saying.
The assistant's conduct was "completely unacceptable", Markus Hünig, president of the Zurich Bahnhofstrasse Association, told the Tages-Anzeiger newspaper.
Hünig said he had never heard of anything like it.