The club did not specify a timeline for his return, but Marca reported Bale could be out of action until December.
Since signing a lucrative new six-year contract with Madrid over a year ago, Bale, 28, has featured in just 24 matches as an ankle operation last November was followed by calf strains and now a thigh problem, which is expected to keep him out for another month.
"He has been diagnosed with a fibrillar rupture in the middle third of the adductor longus muscle of the mentioned leg. Update pending". "His recovery will continue to be assessed".
Despite his return to training in recent days, Bale did not link up with Wales for their worldwide friendly matches against France and Panama on the request of Real head coach Zinedine Zidane.
Real are eight points behind La Liga rivals Barcelona but Zidane is hopeful the possibility of having Bale, Benzema and Ronaldo available after the worldwide break can aid their bid to retain the Spanish title.
The former Tottenham Hotspur man tore a muscle in his calf at the beginning of October, leaving him ineligible to compete in important matches for both club and country; and it's looking like he could miss several more games.
The Wales global has sustained another injury setback and is expected to be out for close to a month.