The club confirmed Wednesday the Belgian shot-stopper suffered a "Grade 1 injury in the left iliac muscle" and that "his recovery will be monitored."
However, Spanish daily Marca estimates Courtois will miss 10 days of action.
Backup goalkeeper Keylor Navas - who reportedly signed a contract extension with Los Blancos - will be called upon in the Copa del Rey against Leganes and in La Liga at Real Betis.
Marca's timescale gives Courtois a chance to return for the big fixture against Sevilla on Jan. 19.
Navas' last appearance for the reigning European champions came Oct. 23 in the Champions League against Viktoria Plzen.