When the prankster said he preferred Scotch, the Governor replied: "I will drink the martini and order another two.
Apparently that was Eddie George's daily in take... before lunch".
Eddie George, who died in 2009, was Governor of the Bank for a decade until 2003.
The hoax emailer 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 stores his "crystal glasses" low down, which would enable Mr Carney to "admire" the bar staffs' "enchanting dexterity".
Carney responded: "Sorry Anthony. Not appropriate at all."
Asked by The Telegraph why he had turned his sights on the Governor, the prankster said: "I targeted him because I saw the Bank of England as a bastion of all things financially secure and proper in this country.
"With so much tradition, were they as antiquated behind the scenes - or were they at the forefront of online/offline security? I don't think my parlour trick proved they were incapable, it did prove their net needs smaller holes though."
A Bank of England spokesman confirmed the authenticity of the email exchange but declined to comment on whether Threadneedle Street will be overhauling its computer security systems as a result of the hoax.
However, it is understood that the Bank continually reviews its cyber security measures.
A fortnight ago, Barclays chief executive Jes Staley was caught out by the same prankster, who at the time described himself as an unhappy customer of the bank.
The hoax took place just hours after Barclays' annual general meeting, when Mr Staley was heavily criticised by shareholders for embroiling the bank in scandal after it emerged last month that he had broken rules designed to protect anonymous whistleblowers.
The prankster emailed Staley purporting to be Barclays chairman John McFarlane. In the subsequent exchange the chief executive gushingly thanked the man he thought was his chairman for defending him during the AGM.
Barclays is in the midst of rolling out a system that alerts its employees if they are responding to external email addresses, a measure that is likely to prevent Staley from falling for a similar hoax in future.