It was initially hoped that Bale could be back in action within two to three months after suffering the injury to the peroneal tendons in his ankle during Real's 2-1 Champions League win at Sporting Lisbon last week.
However, after undergoing surgery in London on Tuesday, Madrid sports daily AS reported the Welshman is unlikely to return before April.
As well as a huge blow to Madrid's hopes in La Liga, Copa del Rey and Champions League, Bale's absence could prove fatal to Wales' chances of qualifying for the World Cup for the first time since 1958.
After a glorious run to the semi-finals of Euro 2016, Chris Coleman's side trail Group D leaders Republic of Ireland by four points ahead of the sides meeting in Dublin on March 24th.
Bale is certain to miss Saturday's El Clasico against Barcelona, the Club World Cup later this month and the first leg of Real's last 16 Champions League tie.