The hacker, named "Guccifer," threatened to publish the electronic exchanges between Powell, 76, and Corina Cretu, 46, who now is a member of the European Union Parliament, the British newspaper The Daily Telegraph reported Friday.
In the emails, which Powell described as being "of a very personal nature," Cretu calls him the love of her life, investigative website TheSmokingGun reported.
Cretu was a member of the Romanian delegation that greeted Powell and President George W. Bush when they visited Bucharest in 2002. She was also part of a Romanian delegation to Washington in March 2004.
Powell and his wife, Alma, have been married for more than 50 years.
"This was a friendship that electronically became very personal and then back to normal," Powell said in a statement to TheSmokingGun in response to the hacking and threat.
Powell said he and Cretu stayed in touch after he left the State Department in 2005.
"I frequently gave her advice on the prospects of finding a position with the U.N. or other international organizations," Powell told TheSmokingGun. "Over time the emails became of a very personal nature, but did not result in an affair."
Cretu married last year.
"There was no affair then and there is not one now," Powell said in the email.
Guccifer has targeted email accounts of officials in the administrations of Bill Clinton, Bush and Barack Obama. Former FBI agents, and friends and family of the Bushes also have been targeted, the Telegraph said.
Guccifer tried to post emails on Powell's Facebook page, then put a link to the documents, the Telegraph said.
At one point, Powell said he warned Cretu the hacker "may have lots of your emails, maybe not" and advised her to "to delete all between us," the Telegraph said
In his email to TheSmokingGun, Powell said, "In light of what was happening it seems obvious to ask Ms. Cretu to delete emails."
On Thursday, Guccifer uploaded a second update to the general's Facebook page that contained a link to emails and photos lifted from Cretu's recently hacked Yahoo! email account, TheSmokingGun reported.