Carvajal has been suffering from muscular overload this week, and the Spain international is therefore not risked ahead of a busy period, with Los Blancos boss Carlo Ancelotti leaving him out of the squad.
Odriozola, meanwhile, picked up an injury during Real Madrid's Copa del Rey contest with Cacereno earlier this week, and the issue has ruled the defender out of the trip to Villarreal.
Mariano is also on the sidelines, with the striker missing a third straight match for the reigning European and Spanish champions due to an ankle injury that he picked up during a training session.
There had been some concern over the fitness of Thibaut Courtois, who was not involved in the Copa del Rey game with Cacereno due to a knock, but the Belgium international has been declared fit.
There are also returns for Toni Kroos, Karim Benzema, Vinicius Junior, Luka Modric and David Alaba, who were not involved in the team's last match in the cup.
Ancelotti is expecting to face a different Villarreal this weekend, with the Yellow Submarine changing their style under the management of Quique Setien, who replaced Unai Emery at the helm.
"Villarreal have changed a bit with Setien. They play very well and with a very clear identity. I think it will be an entertaining game because we want to play a good match," the Real Madrid boss told reporters during his pre-match press conference.
"The squad is good and I see the team focused and motivated. Setien likes attacking football with good positioning of the players on the pitch. It's going to be an open game and to win there we have to bring our best."
As expected, Ancelotti has also confirmed that there will be wholesale changes from the side that took to the field against Cacereno.
"Most of those who didn't play against Cacereno will play. For every game, I will choose the best players possible. Also in the Super Cup, which is an important trophy for us," the Italian added.
Real Madrid will take on Valencia in the semi-finals of the Spanish Super Cup on January 10 ahead of a potential final against Barcelona or Real Betis four days later.
Real Madrid squad vs. Villarreal:
Courtois, Lunin, Lopez; Militao, Alaba, Vallejo, Nacho, Vazquez, Rudiger, Mendy; Kroos, Modric, Camavinga, Valverde, Tchouameni, Ceballos; Hazard, Benzema, Asensio, Vinicius, Rodrygo