She said an assistant refused to serve her in an upmarket handbag shop in Zurich.
Winfrey, one of the world's richest women, was apparently told the bags on display were "too expensive" for her.
Her claims, made to a US television programme, come amid a political row over plans by some Swiss towns to ban asylum-seekers from some public places.
The BBC's Imogen Foulkes in Berne says human rights groups have likened the plans - which include banning asylum-seekers from swimming pools, playing fields and libraries - to apartheid.
Proof
Winfrey, who stars in Lee Daniels' new film The Butler, visited Zurich last month to attend singer Tina Turner's wedding. The Oprah Winfrey Show is not shown in Switzerland.
"She said: 'No, no, no, you don't want to see that one. You want to see this one. Because that one will cost too much; you will not be able to afford that,'" Winfrey, appearing on the U.S. television program "Entertainment Tonight," quoted the clerk as saying. "And I said, 'Well, I did really want to see that one.' And she refused to get it."
Winfrey said she left the shop calmly without arguing, but that the experience was proof that racism continues to be a problem.
"There's two different ways to handle it," she said. "I could've had the whole blow-up thing... but it still exists, of course it does."
Her claims are a public relations disaster for Switzerland, our correspondent says.
About 48,000 people are currently seeking asylum in Switzerland. It has twice as many asylum seekers as the European average.
Officials say the curbs, which will also see asylum-seekers housed in special centres, are aimed at preventing tensions with residents.
The country's asylum laws were tightened in June.
Apologies rolling in
Swiss tourism officials and the boutique owner were quick to offer apologies on Friday.
"We are very sorry for what happened to her, of course, because we think all of our guests and clients should be treated respectfully, in a professional way," Daniela Baer, a spokeswoman for the Swiss tourism office, told The Associated Press.
The tourism office also posted an apology on Twitter, saying "this person acted terribly wrong."
Boutique owner Trudie Goetz told the BBC that an assistant had shown Winfrey several other items before the "misunderstanding."
The newspaper Blick described the bag as a crocodile-leather Tom Ford design named for actress Jennifer Aniston, a fan of the American designer. It quoted Goetz as saying the bag was priced at 35,000 Swiss francs.
"I have to admit that the employee is Italian. Of course, she speaks English, but not as well as her mother tongue," Goetz said in a video interview on Blick's website. "It was a real misunderstanding."
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