The world-record signing was due to make his home debut for the La Liga club on Sunday when they welcomed Getafe to the Bernabeu.
But that plan was curtailed when the 24-year-old felt discomfort in the pre-match warm-up, and Real have now confirmed the nature of the problem.
"After the tests carried out today on Gareth Bale at the Sanitas La Moraleja hospital, fatigue in the left thigh muscle was found. It will be treated," a statement released on the club's official website read.
Despite Bale's absence, Real ran out comfortable winners over their city neighbours, with goals from Pepe, Isco and a Cristiano Ronaldo brace securing a 4-1 victory.
No timescale has yet been given for Bale's return, although manager Carlo Ancelotti said he was likely to miss Wednesday's fixture at Elche after Sunday's match.
But the Italian went on to indicate he is hopeful the Welshman will return when Real entertain local rivals Atletico Madrid on Saturday.
‘It was without a doubt one of the most important matches that I played in my career. It wasn’t just Champions League football – it was a whole club at stake’: Ex-Chelsea star opens up on key game which changed the Blues' fortunes forever
'I was Arsenal captain and really enjoyed it, but when Man City come calling, you have to listen': England international reveals reason for swapping London with Manchester
