Left-back Mendy was replaced after just 14 minutes of Sunday's 2-0 win over Espanyol, which delayed Barcelona winning the LaLiga title.
The France international will undergo surgery in the coming hours after suffering his 16th injury since joining Madrid from Lyon in 2019.
"Following tests carried out today on our player Ferland Mendy... he has been diagnosed with a rectus femoris tendon injury in his right leg," Madrid said in a statement.
Mendy made his last France appearance in June 2024 and was unlikely to be in contention for a place in Didier Deschamps's World Cup squad.