Bale, 25, has injured an upper thigh muscle and was an unused substitute in Saturday's league win over Levante.
A Real statement did not disclose how long they expect the Welsh forward to be out for, saying: "His progress will be monitored."
Following the Group B match at Anfield, Real host Spanish rivals Barcelona in La Liga's El Clasico on Saturday.
Bale played the full 90 minutes for Wales in both of their recent European Championship qualifying matches, against Bosnia-Hercegovina on 10 October and against Cyprus in Cardiff three days later.
Wales' next Euro 2016 qualifying match is against Belgium on 16 November and the hope will be that Bale is fit to play a key role again.
The former Tottenham player, who joined Real for £85.3m last year, has played 12 matches for the Spanish side this season, scoring five goals.