Medical staff had detected the problem during the Wales winger's medical last month before he signed his contract and was presented at the Bernabeu, the paper said in its Saturday edition, without identifying the source of its information.
The slipped disc was not causing Bale any discomfort but could require surgery at some point, Marca added.
"In response to the information that the newspaper Marca has published today regarding the player Gareth Bale, Real Madrid would like to state the following," the La Liga club said on their website (www.realmadrid.com).
"The information published, claiming that the player has a slipped disc on the L5-S1 vertebrae and a bulge on two others, is completely false," the statement said.
"The player does not have a slipped disc, as the club's medical services stated clearly to the newspaper before the information was published.
"Surprisingly, the version the doctors offered this media outlet on Thursday 10 October has been omitted.
"The player Gareth Bale has a small chronic disc bulge, which is extremely common among football players and by no means prevents him from carrying out his professional activity normally."
Bale became the world's most expensive player when he joined Real from Tottenham Hotspur for a fee of 100 million euros ($136 million) at the end of the transfer window.
The protracted negotiations over his move disrupted his preparations for the season and although he scored on his debut in a 2-2 La Liga draw at Villarreal last month he has barely played since.
Coach Carlo Ancelotti has said the thigh injury is not serious and he hopes to have Bale back after the international break for Real's La Liga match at home to Malaga next Saturday.
They host Italian champions Juventus in the Champions League the following Wednesday before playing at arch rivals Barcelona in Spain's 'Clasico' on Oct. 26.