The England midfielder, 20, was forced off after scoring two goals in Saturday’s 4-0 La Liga win over Girona.
The Spanish club have not put a timescale on his return and say his recovery will be “monitored”.
“There’s no Bellingham, but without him, we won four out of four,” said Real boss Carlo Ancelotti.
“These injuries have been an opportunity to be more motivated. We can do well against Leipzig.
“We’re on a good run, motivated, in a competition that we like a lot.”
Bellingham’s double made it 20 goals in 31 games in all competitions since his summer move from Borussia Dortmund.
Vinicius Jr and Rodrygo were also on target for Ancelotti’s side at the Bernabeu to open up a five-point lead at the top of the table.
After Tuesday’s tie with Leipzig (20:00 GMT), Real face La Liga games away at Rayo Vallecano and at home to Sevilla before the end of February, with the return leg against Leipzig scheduled for 6 March.