Real captain Carvajal came back from injury to play as a substitute in Madrid's 2-1 win over Barcelona on Sunday.
But the 33-year-old defender will miss the Champions League trip to Liverpool next week, and is likely to be sidelined for Manchester City's visit to the Santiago Bernabeu on 10 December.
"He has been diagnosed with the presence of a loose body in his right knee joint. Carvajal will now undergo an arthroscopy," said Madrid in a statement, without specifying his expected absence period.
Carvajal suffered a severe knee injury in the same leg in 2024 and had an operation, which kept him out for most of last season.
Spanish media reports suggested the Spanish right-back could miss between six and 10 weeks, meaning he will not feature in his country's upcoming World Cup qualifiers in November.