The Real Madrid centre-back had a scan that confirmed the fracture and has left the national team's training camp, Real said in a statement on their website.
The Spanish club did not say how long he might be sidelined.
Midfielder Xabi Alonso, Albiol's Real team-mate, trained normally in Sunday's evening session despite sustaining a gashed shin in Friday's 2-0 win against Czech Republic.
"Alonso trained without any apparent discomfort and said he felt fine, although he was wearing a large bandage on his right leg," the Spanish football federation (RFEF) said on its website.
Full-back Sergio Ramos, another Real player, trained apart from the rest of the squad after being substituted at half-time in Prague as a precaution but should be back with his team mates for Monday's session in Alicante, the RFEF added.
