Valverde featured in Madrid's 4-1 defeat to Valencia in LaLiga on Monday (AEDT) before he was replaced by Toni Kroos in the 76th minute.
A medical bulletin issued by Madrid on Tuesday did not give an indication of when head coach Zinedine Zidane expected to have the player available again.
The statement said: "Following tests carried out on our player, Federico Valverde, by Real Madrid medical services, he has been diagnosed with a fracture in the posterior tibial bone in his right leg.
"His recovery will continue to be assessed."
However, the 22-year-old Uruguay international is set to miss his country's forthcoming FIFA World Cup qualifiers with Colombia on November 13 and against Brazil four days later.
Valverde has made 11 appearances for Madrid in all competitions this season and scored three goals.
Madrid's next game is away to Villarreal in LaLiga on 22 November.