Madrid says Albiol broke the bone when colliding with a teammate during the session and has been forced to drop out of the squad to face Scotland on Tuesday.
Club doctor Oscar Celada says the bones were not displaced by the fracture. The club did not say how long Albiol will be out.
Real Madrid has a home league match against Real Betis on Saturday.
Albiol joins Portugal defenders Pepe and Fabio Coentrao on Madrid's injury list.