Ms McEnany told Fox News's Hannity that she has been “permanently” banned from her personal account after redistributing the article, which both Facebook and Twitter have restricted access to over concerns about its veracity.
"It’s not a temporary blockage," said Ms McEnany. "When I log on to my Twitter account, it says I'm permanently banned".
As of Thursday afternoon, Ms McEnany's personal page was still visible on Twitter. Usually, when the social media firm permanently bans a user from its site, their profile is no longer visible to the public.
When Twitter banned the far-right British commentator Katie Hopkins in June this year her page disappeared from the platform.
A spokesperson for Twitter told The Independent users who violate its hacked materials policy can return to the platform once the offending tweet has been removed.
Ms McEnany went on to tell Hannity that Twitter "essentially have me at gunpoint", before claiming that the social media firm had instructed her to delete the post before she could get back into her account.
Her row with Twitter relates to a story published by the New York Post on Wednesday.
The article is based on emails purportedly obtained from a laptop that Hunter Biden had supposedly left behind for repair in a Delaware shop in April 2019.
An email from 2015 suggests Hunter Biden arranged for a top executive at a Ukrainian energy firm to meet with his father, the then-vice president when he was in charge of US policy toward Ukraine.
“Dear Hunter, thank you for inviting me to DC and giving an opportunity to meet your father and spent [sic] some time together. It's realty [sic] an honour and pleasure,” says the email, allegedly written by Vadym Pozharskyi, an adviser to the board of Burisma.
Watch: Twitter briefly restricts Trump campaign account
Hunter Biden in 2014 became a board member of Burisma, which news reports at the time suggested was a conflict of interest given his father's position.
Mr Biden has said he did not discuss Burisma with his son. The email is not specific about the nature of the meeting.
Nevertheless, Republicans who have long sought to tie the vice president to his son's business interests claim the alleged email is proof that the former VP used his influence to help his son.
The Post claims it was a “smoking-gun" email.
Both Facebook and Twitter have restricted access to the controversial story, sparking outrage among Republicans.
Twitter says the emails cited in the piece may have been obtained illegitimately, and therefore the story breaches its hacked materials policy.
"In line with our Hacked Materials Policy, as well as our approach to blocking URLs, we are taking action to block any links to or images of the material in question on Twitter," the company said in a statement.
Twitter further explained its position in a series of messages posted by CEO Jack Dorsey.
Facebook also placed restrictions on the piece, saying there were questions about its validity.
“This is part of our standard process to reduce the spread of misinformation,” said Facebook spokesperson, Andy Stone.
Watch: Former Ohio Governor John Kasich says Trump ‘hurt his own supporters’