Club medical staff said that the Brazilian was suffering from inflammation of the big toe on his left foot and would undergo physiotherapy to deal with the problem.
Ronaldo turned up late for training on Tuesday after being delayed on his return from the celebrations at a secluded chateau near Paris and also missed the first 15 minutes of the session on Wednesday.
Sports daily Marca said that the 28-year-old would be fined by the club because of his late arrival.
Ronaldo turned up on time on Thursday, but pulled up after a few minutes and it now looks unlikely that he will play against Bilbao. England striker Michael Owen will take his place in the starting line-up if he fails to recover in time.
Owen's England team mate David Beckham and captain Raul, who both complained of some minor muscle pain after playing in the tsunami benefit match at the Nou Camp, trained normally on Thursday.
Real play Serie A leaders Juventus at the Bernabeu next Tuesday in the first leg of their Champions League knockout tie.
