Bale sustained the injury in the White Angels' last training session at the Estadio Santiago Bernabeu on Saturday, a day before their game against Celta on Sunday.
Bale was seen limping onto the team bus on Saturday evening with his thigh strapped as he was left out of the matchday squad for the Celta game before attending the club's Valdebebas training ground on Monday for tests.
After the test conducted on Monday morning it was revealed that the former Tottenham Hotspur player has suffered a long-term injury in his right hamstring.
Bale will miss Real Madrid's Champions League game at Inter Milan on Wednesday.
Becoming out of favour at Real Madrid during Zinedine Zinedine's era as the head coach, Bale embarked on a loan move to former side Tottenham Hotspur.
And with the return of Carlo Ancelotti to replace departed Zidane, Bale seems to be cementing a place in the starting line-up at Madrid, after starting first three games of the season against Alaves, Levante and Real Betis, scoring in the 3-3 draw with Levante on Aug. 22.
Real Madrid after missing out on the LaLiga title to Atletico Madrid last season will hope to win the accolade this time around.
Bale scored 11 goals with two assists in twenty Premier League fixtures during his loan spell at spurs.
