Skrela came off after just a few minutes in the 22-3 quarter-final triumph at Vicarage Road and hasn't featured in Clermont's two Top 14 games since that success.
A Heineken Cup winner with Toulouse in 2010, Skrela will have surgery later today to deal with a hematoma on his thigh.
Clermont's medical team had worked tirelessly in an attempt to cure the problem without having to resort to an operation but the 33-year-old hasn't made the progress his club had hoped for.
It is not yet known how long Skrela will be sidelined for, although he is expected to be unavailable for weeks rather than days.
His availability for the Heineken Cup Final on Saturday, May 19 will be assessed nearer the time if Clermont see off Leinster this weekend.
Skrela's absence will almost certainly lead to Australian playmaker Brock James wearing the No10 shirt against the reigning European Champions.
James played a starring role after replacing Skrela against Sarries, kicking 17 points and picking up the Heineken Man of the Match award.
In other injury news, flanker Julien Bardy has been declared fit and could be included in the Clermont matchday 23.