Both players were substituted after sustaining problems during Madrid's 4-2 La Liga win at Celta Vigo on Sunday.
Madrid said in a statement on Monday that Nacho had suffered a dislocation in his right knee and Casemiro had sprained his ankle.
The European champions are already missing defenders Marcelo, Raphael Varane and Dani Carvajal through injury, as well as striker Mariano Diaz.
(Reporting by Rik Sharma; Editing by Christian Radnedge)