Narraway, who had been drafted in as injury cover for Tom Wood, suffered the injury towards the end of England's open training session in Leeds.
England's interim head coach Stuart Lancaster had decided to delay any decision until after the Saxons' game against the Ireland Wolfhounds in Exeter this evening.
The Saxons won 23-17 and Thomas Waldrom, the leading contender to replace Narraway, capped a storming individual performance with England's second try.
Ben Morgan is the only specialist number eight in the England squad, although Chris Robshaw, Phil Dowson and Calum Clark are all versatile back row operators.
The England squad reconvene on Sunday night to begin the build-up to their opening RBS 6 Nations game, against Scotland at Murrayfield next Saturday.
Lancaster will name his captain on Monday and then cut his squad down from 32 on Tuesday night, with the exact starting line-up and bench to be announced on Thursday.
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