Eddie George, who died in 2009, was Governor of the Bank for a decade until 2003.
The prankster, who used a hoax email address, then invited Mr Carney to a party next month and said he had “hired some rather dashing bar ladies (is that PC?!)”.
He told the Governor he keeps his “crystal glasses” low down so that Mr Carney could admire the bar staffs’ “enchanting dexterity”.
Mr Carney responded: “Sorry Anthony. Not appropriate at all.”
A Bank of England spokesman confirmed the authenticity of the email exchange but declined to comment further.