Marienne Ferguson, a 78-year-old who fled the Nazis aged 13 and lost family members in the Holocaust, said the heir to the throne made the controversial remark during a tour of a museum in Canada.
“I had finished showing him the exhibit and talked with him about my own family background and how I came to Canada,” Ferguson told Britain’s Daily Mail newspaper.
“The prince then said: ‘And now Putin is doing just about the same as Hitler’.
“I must say that I agree with him and am sure a lot of people do.
“I was very surprised that he made the comment as I know they (the royal family) aren’t meant to say these things, but it was very heartfelt and honest.”
The remark made headlines around the world, and Russian media said it threatened to further “complicate” relations between Britain and Moscow.
The prince’s office, Clarence House, said in a statement: “We do not comment on private conversations.
“But we would like to stress that the Prince of Wales would not seek to make a public political statement during a private conversation.”
Ferguson gave a similar account of the conversation to the BBC, saying: “He (Charles) made the remark that now Putin is doing some of the same things that Hitler was doing.”
They met as the royal conducted a tour of the Canadian Museum of Immigration in Halifax, Nova Scotia, as part of a four-day trip to Canada with his wife Camilla.
Ferguson told the BBC that it was “just a little remark, I didn’t think it was going to make such a big uproar”.
Members of the royal family by convention do not comment on political affairs, and Queen Elizabeth II, Charles’ mother, has made a virtue of keeping her own counsel.
Charles, the future king, is due to meet with Putin in France on June 6 as part of the commemorations marking the 70th anniversary of D-Day.
There was no immediate official reaction in Moscow.
But popular daily Moskovsky Komsomolets wrote on its website that the remarks “risk triggering an international scandal and complicate the already clouded relations between Great Britain and Russia.”
It said the timing of the remarks was “badly chosen” ahead of the D-Day anniversary events, which will also be attended by the queen.
The prince’s comments echo those reportedly made by former US secretary of state Hillary Clinton in March, and reflect Western frustration with Russia over Ukraine.
Russia’s annexation of Crimea in March set off the worst diplomatic crisis in the West’s relations with Moscow since the end of the Cold War.
It has been followed by uprisings and fighting in eastern Ukraine that have raised concerns of a civil war erupting on Europe’s doorstep.