The letter was sent to Mr Ramaswamy's campaign by record label BMI, dated August 23.
“BMI has received a communication from Marshall B. Mathers, III, professionally known as Eminem, objecting to the Vivek Ramaswamy campaign's use of Eminem's musical composition (the “Eminem Works”) and requesting that BMI remove all Eminem Works from the Agreement,” BMI says in the letter first reported by the Daily Mail.
The letter also stated that the notice would immediately begin and BMI would consider any performance of Eminem's music by Mr Ramaswamy as a breach of the agreement.
The notice came 11 days after the Republican candidate launched into a performance of the song Lose Yourself at the Iowa State Fair.
“Will The REAL Slim Shady Please Stand Up? He didn’t just say what I think he did, did he?” Mr Ramaswamy wrote on Twitter in response to the letter.
Mr Ramaswamy has been outspoken of his appreciation for Eminem's music.
In an interview with The New York Times, Mr Ramaswamy said he and Eminem had different upbringings but identified with being an underdog.
While at Harvard, Mr Ramaswamy would perform under the alter ego “Da Vek”. In a 2006 interview with The Harvard Crimson, Mr Ramaswamy said Lose Yourself was his life's theme song.
The Republican candidate, an entrepreneur with no political experience, has seen a recent rise in the polls and was at the centre of attacks during the party's first debate last week.