Speaking to reporters in Tokyo, Carney said the actions that have caused him to be stripped of his royal titles "necessitate" his removal from the line of succession.
Despite being stripped of his status as prince in October over his close links with the late convicted sex offender Jeffrey Epstein, Andrew, King Charles III's younger brother, remains eighth in line to become monarch.
Charles is the head of state in Canada, which, like Australia, is a member of the Commonwealth of former colonies.
Australian Prime Minister Anthony Albanese wrote to UK Prime Minister Keir Starmer in February to support the push to remove Andrew Mountbatten-Windsor from the line of succession.
NZ's prime minister has also expressed support for Andrew's removal.
Carney, a former governor of the Bank of England, said even though Mountbatten-Windsor is "well down" the line of succession, the "point of principle stands".
The prime minister said there is a process to remove someone from the line of succession, which he said should be followed.
Under the current line of royal succession, Charles' son Prince William is heir to the throne and his three children - Prince George, Princess Charlotte and Prince Louis - are next.
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