The France international netted his fifth league goal of the campaign in the narrow success over Alaves, but he was replaced in the 80th minute of the contest due to an injury issue.
Los Blancos head coach Carlo Ancelotti said after the match that Mbappe was "fine", claiming that the summer arrival was only suffering from 'overload'.
"He's fine. He was a little overloaded and he asked me to change to avoid any problems," Ancelotti told reporters in his post-match press conference.
However, according to Relevo, there is genuine concern from the club that Mbappe will not be available for the league game against Atletico this weekend.
Mbappe 'a genuine doubt' for Madrid derby
Real Madrid are yet to conduct tests, but the report claims that his availability against Atletico 'cannot be guaranteed', and the club are not prepared to take any risks when it comes to his fitness.
Los Blancos were 3-0 ahead against Alaves early in the second period of Tuesday's clash, but they had a late scare at Bernabeu, conceding twice in the latter stages, as it finished 3-2.
Mbappe has now scored seven goals and registered one assist in nine appearances for Real Madrid since arriving at the club on a free transfer over the summer.
Real Madrid - unbeaten in all competitions this season - are currently second in the La Liga table, one point behind leaders Barcelona, although the Catalan outfit do now have a game in hand.
Who could replace Mbappe against Atletico?
Eduardo Camavinga is being tipped to recover from a knee injury in time for the Madrid derby, so he could provide an option to replace Mbappe in the XI, with Ancelotti switching to a four-man midfield, leaving Vinicius Junior and Rodrygo in the final third of the field.
However, it would be a surprise if Camavinga came straight into the side considering the fact that he has not made a single appearance this season.
Endrick is the obvious option to earn his first start if Ancelotti keeps his 4-3-3 formation, but Arda Guler and Luka Modric will also be in the manager's thinking.
Jude Bellingham played as a number 10 for the majority of last season behind Vinicius and Rodrygo, meanwhile, so there are plenty of options for Ancelotti when it comes to replacements.
However, at this stage, Mbappe has not been ruled out of the Madrid derby, with the official medical tests yet to be completed, so the ex-Monaco youngster could yet be available.