Carvajal has sustained a grade two tear to his right thigh and, according to reports in Spain, will be out of action for at least a month.
The right-back played the full 90 minutes as Madrid suffered a shock 4-1 loss to Ajax on Wednesday (NZDT) and consequently crashed out of the UEFA Champions League at the last-16 stage.
Vazquez hobbled off before the half-hour at the Santiago Bernabeu and Madrid, who return to action against Real Valladolid on Sunday, announced he suffered a grade one strain to his left hamstring.
It is therefore unlikely either player will be fit to feature for Spain when they begin their Euro 2020 qualifying campaign with matches against Norway and Malta this month.
Madrid sits 12 points adrift of LaLiga leader Barcelona after a 1-0 loss at home to Ernesto Valverde's men last weekend.
Carvajal and Vazquez join Vinicius Junior in the treatment room after it was confirmed on Wednesday the Brazilian had torn calf ligaments in his right leg, ruling him out until the final stages of the season.