Initial reports in Spain suggest the centre-back could be out of action for up to two months after the operation on his left knee.
The 34-year-old has been out since playing the full 90 minutes of their 2-1 loss to Athletic Bilbao in the Supercopa de Espana on January 14.
In his absence, Zinedine Zidane's side suffered a humiliating Copa del Rey exit to Alcoyano and lost 2-1 to Levante in LaLiga after beating Deportivo Alaves 4-1.
In all competitions in 2020-21 prior to Saturday's meeting with Huesca, Madrid have won just 40 percent of matches without Ramos compared with 61 per cent when he has played.
Indeed, they have won four and lost five of the 10 games without their captain, scoring fewer goals (1.5 compared with 1.8) and conceding more (1.3 compared to 1.0).
Such is the influence of Ramos on their play, Madrid's average possession drops from 63.1 percent to 56 percent in his absence, while they attempt two fewer shots and concede two more crosses per game.
The veteran Spain international scored 11 goals in 35 appearances in LaLiga last season as he inspired his side to the title but has managed only two goals in 14 league games in 2020-21.
His future beyond this term remains unclear, with his contract expiring at the end of the season and Paris Saint-Germain and Manchester United reportedly interested in signing him.
After taking on Huesca, Madrid face Getafe, Valencia and Real Valladolid before the first leg of the European tie with Atalanta in Bergamo on February 24.