The Portuguese forward ended a four-match goal drought with a hat-trick at the Bernabeu but had to leave the pitch with just over 10 minutes remaining, reducing Real to 10 men as they had used all three substitutes.
Jose Mourinho's side were already seven goals ahead and their biggest win of the season cut Barcelona's lead at the top back to seven points with 26 matches played after Lionel Messi had given the champions a 1-0 win at Valencia on Wednesday.
"It's better not to take risks. I don't think I'll be available for Sunday's match," Ronaldo, who is level with Argentina forward Messi at the top of the La Liga scoring chart on 27 goals, told reporters after the match.
Real said on Friday that a scan had confirmed the injury and Ronaldo would be sidelined for 10-15 days.
The 26-year-old could also miss the La Liga game at home to Hercules on March 12 and the Champions League last-16, second leg against Olympique Lyon four days later.
Sunday's game at Racing's Sardinero stadium is a chance for the club's new Indian owner Ahsan Ali Syed to see at first hand how his team fares against one of La Liga's two dominant clubs.
Ali Syed, the chairman of investment company Western Gulf Advisory who became Racing's majority shareholder at the end of January, told Reuters last month he aims to make the club a "third force" in Spain alongside Real and Barca, who host struggling Real Zaragoza on Saturday.
Racing, in 12th on 30 points, five above the relegation places, are undefeated in six matches since his arrival.
IMPORTANT STEP
New coach Marcelino Garcia, who replaced the sacked Miguel Angel Portugal on February 9, appears to be more focused for the time being on securing their place in the top flight than challenging the world's two richest clubs.
"A win would be an important step, not a definitive one, to make sure of our survival," he told a news conference on Wednesday.
"The match will be tough, although thanks to the points we already have it will be more important for them.
"Their need could be a virtue but the longer the match goes on the more anxious they might get and that could help us."
Third-placed Valencia, who are 13 points behind Real, play at Real Mallorca on Saturday, while Villarreal, a point back in fourth, are at eighth-placed Atletico Madrid in Saturday's late kick-off.
Barca coach Pep Guardiola may not be able to attend Saturday's match against Zaragoza after suffering a painful spinal disc hernia.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
