The Argentine midfielder, who returned to action on Saturday after a six-week absence, lasted just 36 minutes before he was forced out of the Aston Villa derby with a shoulder injury.
Baggies boss Steve Clarke said he was unsure when the summer signing would return to his side, and is hoping to avoid further injury setbacks in the coming months.
"Claudio has damaged his shoulder. We are not sure how serious it will be, so it's fingers crossed," he said.
"It's a blow to him after just coming back from injury but we have got 10 days to the next game against Everton (on January 30).
"He was doing the job great for us as a defensive midfielder until he got injured and we have missed him a little bit.
"We are hopeful we will get a few more players out of the treatment room in the near future."