- Tag results for Gareth Bale
The 29-year-old had hoped to recover for his country's trip to Dublin on Tuesday, but Wales manager Ryan Giggs had already admitted he didn't expect the forward to be back in time.
Kevin De Bruyne was nominated for helping his club win the Premier League and his country reach the World Cup semi-finals.
Madrid have gone three games without scoring, after their surprise Champions League loss to CSKA Moscow on Tuesday followed a draw against Atletico Madrid and defeat to Sevilla.
Bale picked up a thigh injury during the goalless draw with Atletico Madrid on Saturday and had to come off at half-time.
Bale has scored four goals in his last seven games for Real and any absence would be a major blow.
Isco curled in a terrific free-kick just before half-time at the Santiago Bernabeu, with Bale powering in a second and Mariano Diaz striking late as Real made a convincing start to their campaign.
If the summer had gone differently, Gareth Bale might have been on a plane to Switzerland on Monday to play for Manchester United against Young Boys.
Gareth Bale is thriving in the absence of Ronaldo and Madrid have three wins from four La Liga matches.
Rejuvenated under new coach Julen Lopetegui and, perhaps, liberated by Cristiano Ronaldo's departure, Bale and Benzema impressed again.
Bale became Wales's top goalscorer earlier this year when his 29th international goal took him past Ian Rush's record.
Real Madrid have yet to sign a direct replacement for the Portuguese superstar Ronaldo, who switched to Juventus in July after scoring 450 goals in 438 games over nine seasons at the club.
Seeking their second win of the new La Liga season, the European champions went behind after Borja Garcia opened the scoring for Girona with a superb goal after 17 minutes.
Bale's cross was headed in by Dani Carvajal for Real's opening goal in their first match of the new campaign in La Liga, and he later scored his side's second at the Santiago Bernabeu.
Real Madrid ensured the three points at the Santiago Bernabeu with a 20th-minute goal from Dani Carvajal and a Gareth Bale strike on 51 minutes.
Atletico Madrid warmed up for the Super Cup in Tallinn in Estonia with a 1-0 loss to Inter Milan at their Metropolitano stadium home.