During an interview with Channel 4 News the North Shropshire Conservative said that "people come up to me on the trains, on the Tube saying just get on with it", regarding Brexit.
Louise Haigh, Labour MP for Sheffield Heeley and Shadow Policing & Crime Minister, had then retweeted the interview to the popular Twitter account "Didn't Happen of the Year Awards", with the comment: "No one is talking to anyone on the tube."
The account pokes fun at what it considers 'fake news', retweeting posts where people are accused of making up what they are saying.
A number of celebrities have been retweeted by the account, including Brazilian legend Pele, who was called out after posting: "Once, in a match in Senegal, the goalkeeper cried so much after I scored that he had to be substituted! He had lost a big bet!"
In response to her tweet, Mr Paterson sent a formal letter to Ms Haigh criticising what he branded a "stunt".
I have written to @LouHaigh after she nominated me for the @_DHOTYA Awards. The man who approached me unsolicited on the Tube encouraging me to continue urging the Government to deliver Brexit gave me his card and she is most welcome to come to my office to see it for herself! pic.twitter.com/yOMoTnbMIN— Owen Paterson (@OwenPaterson) March 20, 2019
He said the encounter had taken place, offered to provide evidence, and called on her to withdraw her nomination to the account.
His letter stated: "I note that on Twitter yesterday you nominated my comments about being approached by a member of the public on the London underground for the 'Didn't Happen of the Year' Awards.
"On Monday, a man came up to me unprompted and encouraged me to continue my public comments urging the Government to deliver Brexit on time.
"I am surprised that you did not discuss the matter with me before publicising your stunt. As I said in the House earlier, the gentleman in question even gave me his card. I will not, of course, publish his name as he gave it to me privately, but you are most welcome to come to my office and see it for yourself. I should therefore be grateful if you would withdraw your nomination publicly."
The request does not seem to have had the desired effect, as when asked by the "Didn't Happen of the Year Awards" account if she wanted to withdraw the nomination Ms Haigh said: "I regret nothing."
It is the second time this month that Mr Paterson has written to a Labour MP in recent weeks, after he called on Jeremy Corbyn not to misquote him.
Speaking at Prime Minister's Questions Mr Corbyn had quoted Mr Paterson as saying "only a madman would leave the single market".
In response the Shropshire MP wrote to the Labour leader to over the matter, which Mr Paterson said "is a very common misquotation, frequently repeated on Twitter".
He proceeded to detail the full quote, taken from an interview with Dermot Murnaghan on Sky News, and asked Mr Corbyn not to misquote him again.