The 27-year-old second-row injured an ankle when he scored the first of Wales' two tries as they came from 10-3 down at half-time.
Josh Adams added a superb second to keep their hopes alive of a third Six Nations Grand Slam under Warren Gatland and dash England's aspirations at the same time.
"He's certainly going to be a loss, but any loss is someone else's opportunity," said Wales' kicking skills coach Neil Jenkins.
"Cory was outstanding on Saturday, obviously with his try as well and he's a fantastic player for us.
"He's a good person around the squad as well, (but) we've got some fantastic players in that position as well so it will be quite interesting to see who plays in the last few games."
Possible replacements for the next match against Scotland in Edinburgh and the climax against defending champions Ireland in Cardiff are either Adam Beard and Jake Ball, who have both started matches this season.
Beard and Ball were paired together in the scrum's engine room for the unconvincing win over Italy in the second match of the championship.
Beard started the opening win over France alongside captain Alun Wyn Jones.
Wales coach Warren Gatland - who is stepping down after the World Cup later this year after 12 years in charge - will be boosted by the availability of fullback Leigh Halfpenny, after he came through unscathed for the Scarlets on Sunday after three months out following concussion.
However, Halfpenny's thunder has been somewhat stolen by Liam Williams's man of the match performance on Saturday, though, the latter can also slot in on the wing.
Flyhalf Rhys Patchell and scrumhalf Tomos Williams also look set to be available for the visit to Murrayfield along with tight-head prop Samson Lee.