Alba battled on to finish the 90 minutes in Sunday’s 1-1 draw at Real Sociedad despite suffering the injuries before half-time.
“The tests carried out this morning reveal that Jordi Alba has heavy bruising on his right knee and a strain of his left ankle,” Barca said in a statement.
“How he evolves will determine his availability for the next few games.”
Barca desperately need to end Madrid’s 31-game unbeaten run at the Camp Nou after falling six points behind their eternal rivals at the top of La Liga.
Should Alba not recover in time, French international Lucas Digne will deputise at left-back.
The Catalans also hope to recover Samuel Umtiti and captain Andres Iniesta from injury in time for Madrid’s visit.