The 27-year-old Wales international lasted just 35 minutes of Sunday's El Clasico defeat to Barcelona before limping off the Bernabeu pitch.
A short statement from Madrid confirmed the extent of Bale's injury, saying: "Following the tests carried out on Gareth Bale by the Sanitas Medical Services, the player has been diagnosed with a grade 2 injury in his left calf.
"His recovery will continue to be assessed."
Reports in Spain say Bale is now facing three weeks on the sidelines, which would rule him out of both legs of the Champions League tie - on May 2 and 10 - as well as LaLiga fixtures against Deportivo La Coruna, Valencia and Granada.
It is the latest blow in what has been a frustrating campaign for the former Tottenham man, who has been struck down by several injuries, including a three-month lay-off earlier this season with an ankle problem.
Madrid coach Zinedine Zidane, meanwhile, has defended himself against criticism that Bale was rushed back into the starting line-up too soon, having only recently returned to training following another muscle injury.
The Frenchman told a press conference to preview Wednesday's league clash with Deportivo: "He was 100 per cent fit, he told me. Before the match everything was fine and he was training normally.
"These things cannot be avoided. He wants to play and when you have a very long injury lay-off it is difficult, I know from experience. The recovery time is not the same.
"There are other annoying niggles and this is what is happening to him now. It is minor and we expect him to come back swiftly."
Real were also set to be without captain Sergio Ramos for the match at Deportivo.
The defender was shown a straight red card for his sliding challenge on Lionel Messi, who scored a stoppage-time winner for Barcelona.
The Spanish Football Federation (RFEF) confirmed on Tuesday night that the suspension would only be for one match, meaning Ramos will be available again for the visit of Valencia.
Ramos appeared to sarcastically applaud as he left the pitch and also exchange words with Barcelona's Gerard Pique.
If mentioned in the referee's report, those actions could have seen the ban increased as happened to Barca forward Neymar following his red card at Malaga.
