The prince caused controversy when he told a woman that Putin "is doing just about the same as Hitler" in annexing Crimea in the Ukraine.
Prince Charles and wife Camilla are on a tour of the Commonwealth nation where a former Polish war refugee who met them claims the Prince of Wales likened some Nazi actions in Europe to those of Putin.
Marienne Ferguson was speaking after meeting Prince Charles at a Nova Scotia immigration museum where she works.
Popular Russian daily paper 'Moskovskij Komsomolets' (MK) reacted by saying that the comment risked complicating UK-Russian relations.
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"The heir to the British throne, Prince Charles, risks triggering and international scandals and complicating the already not unclouded relationship between Britain and Russia," it stated.
Clegg told BBC: "I have never been of the view that if you are a member of the royal family somehow you have to enter into some sort of Trappist vow of silence. I think he is entitled to his views."
Prince Charles' office at Clarence House said it would not comment on a private conversation.