During a visit to a cathedral in Staffordshire on Monday, the King was confronted by a individual who questioned him about his brother's links with disgraced financier Epstein.
The protester demanded to know how long the King had been aware about his sibling's association with Jeffrey Epstein, and also questioned whether he had instructed the authorities to "hide" for Prince Andrew.
Amid the heckling, there were large groups of supporters and applause for the King, who was in the region for an event.
Prince Andrew's associations with Jeffrey Epstein have been under intense scrutiny in the past few weeks. The prince, who gave up his titles earlier this month, has categorically denied any wrongdoing.
"For how long have you known about Prince Andrew and Epstein? Have you asked the authorities to cover up for Andrew?"
The King ignored the questions but carried on meeting fans, some of whom chanted "Long live the King". One supporter can be overheard asking him for a hug.
Another woman outside the venue was also observed telling the protester to "go away" and to "shut up".
The controversy over the Duke of York's links to Jeffrey Epstein has been brought back into focus by misconduct allegations detailed in Virginia Giuffre's recently released memoir.
In the memoir, Ms Giuffre alleges she had sex with the prince on three separate occasions, including once with Epstein and "eight other young girls"
Andrew, who reached a out-of-court agreement with Ms Giuffre in recent years, has repeatedly denied any misconduct. In a previous interview, he told BBC Newsnight he did not remember meeting Ms Giuffre "ever", and that they "did not have any sort of sexual contact."
But recently, fresh questions have been raised about how he is able to finance his lifestyle despite not being a working royal.
The revelation that he has only ever paid a nominal fee on his Windsor mansion has heightened the examination over his living arrangements - even though he made significant contributions up front, including for improvements.
The political party said he should be called in front of MPs to give evidence about his lease of his lodge.
But last week, the authorities declined to give MPs time to discuss the royal's status or his residence, despite growing pressure for scrutiny.
The royal household has not commented on whether Prince Andrew might move out of his current residence - or where he might reside.
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