Madrid said in a statement on Wednesday that the Belgian had a grade one injury in his left hip muscle, without stating for how long he would be ruled out.
Spanish media reports said Courtois would be out for around 10 days, ruling him out of Sunday's trip to Real Betis in La Liga as well as both Copa del Rey games against Leganes.
The Belgian was expected to be on the bench for Wednesday's first-leg match and the return leg on Jan. 16, with Keylor Navas playing instead.
Courtois's injury setback comes one day after Germany midfielder Toni Kroos was diagnosed with a thigh problem, ruling him out for between three to four weeks and meaning he will miss a crunch league game against high-flying Sevilla on Jan. 19.
Real winger Lucas Vazquez is suspended for Sunday's visit to Real Betis after being sent off in last week's 2-0 defeat to Real Sociedad, which left Santiago Solari's side fifth in La Liga and 10 points behind leaders Barcelona.
Record signing Gareth Bale is currently sidelined with a groin strain and is not due back until the end of the month, while fellow forwards Marco Asensio, Mariano Diaz as well as midfield anchor Marcos Llorente are also unavailable due to injury.
(Reporting by Richard Martin; Editing by Toby Davis)
