A balaclava-wearing man threatened the ex-prince while he was out for an evening walk with his dogs on Wednesday, British media reported.
The man allegedly waited for Andrew, jumped out of a car and verbally threatened him and a security guard.
Police were called and found the man was carrying a weapon; the exact type has not been made public. Police do not suspect this is a terrorist crime.
Andrew, King Charles' younger brother, was stripped of his princely title in October last year after several scandals linked to documents released in the criminal investigation into Jeffrey Epstein.
He has been living in a house on the royal family's Sandringham estate in Norfolk in eastern England since February.
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