The Argentinian international returned to the side for Saturday's 2-2 draw against Aston Villa after a six week absence with a hamstring injury.
But he had to be substituted during the latter stages of the first half with a shoulder problem.
Albion head coach Steve Clarke confirmed: "Claudio has damaged his shoulder. We are not sure how serious it will be, so it's fingers crossed.
"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."
Clarke is hopeful Albion will be back to near full strength in the not too distant future.
Strikers Shane Long (dead leg) and Marc-Antoine Fortune (hamstring) plus defender Steven Reid (shin) should be fit to face the Toffees.
Clarke said: "We are hopeful we will get a few more players out of the treatment room in the near future."
- Sports & Recreation