Horsman, 30, has undergone surgery on his left arm after suffering a ruptured bicep and snapped a tendon during his club's 26-21 defeat to Leeds last Friday.
The Warriors confirmed Horsman is not expected to be back in action until the end of February.
At the very least, that would also rule him out of Wales' clash with England at Twickenham and the home games against Scotland and Italy.
Horsman had only just returned to club duty following the World Cup and his absence is also a major blow for Worcester, who are struggling at the foot of the Guinness Premiership without a win this season.
Director of rugby Mike Ruddock said: "We're obviously disappointed but knowing Chris as I do he will try his hardest to prove medical science wrong and get back on the field before the projected timescale."