The guitarist, who was a founder member of the Mancunian band along with frontman Morrissey, denounced the current prime minister's claims that he is a big fan of the band.
Marr wrote on Twitter: "David Cameron, stop saying that you like The Smiths, no you don't. I forbid you to like it. (sic)"
Cameron has previously professed his fondness of the band's music and picked 'This Charming Man' when he appeared on Desert Island Discs.
The group are known for their anti-establishment stance, while Morrissey's debut solo album Viva Hate included the track 'Margaret On The Guillotine', about the imaginary execution of Margaret Thatcher.