Crockett, 29, has made a total of 34 appearances for Warriors, scoring four tries, and the former England Saxons player has also had previous playing spells at Bath and Bristol Rugby.
Head Coach Richard Hill said: "We are all hugely disappointed for Crocks as he had just worked himself into some good form and had featured in the Aviva Premiership for us this season and played in the recent LV= Cup fixtures.
"We now wish him well with his recovery with the medical and rehabilitation staff at Sixways.
"It is a blow for us but we are lucky to have good depth in that area of the squad. Dale Rasmussen and Alex Grove have performed strongly for us in the league and we have Sione Tu'ipulotu, Chris Pennell and Tom Arscott who can play in that position and our new signing Ravai Fatiaki joining us soon so we are not looking to recruit.
"Young players like Andy Short and Charlie Hayter are also keen to impress and this will give them more opportunities for more senior rugby."