The Harlequins star has broken the fifth metatarsal in his left foot, and he will see a specialist in London on Wednesday, accompanied by England team doctor Simon Kemp and Quins' head physiotherapist Steph Brennan.
The injury happened during an open running element of the session, and no contact was involved.
England head coach Brian Ashton said: "I am obviously sorry to hear about David's injury and I wish him a speedy recovery.
"I won't make any decisions about a possible replacement until I receive a full briefing on the consultation tomorrow (Thursday) morning."
Ashton has already ruled uncapped Bristol number eight Dan Ward-Smith out of his World Cup plans after he failed to recover in time from a knee injury.
Centre Mike Tindall (leg) could also miss the final World Cup squad cut - a decision could be made on Thursday - while Mark Cueto (groin), Tom Rees (hamstring) and Peter Richards (back) are also currently battling injuries.
Wing Ben Cohen and prop Julian White, meanwhile, both made themselves unavailable for the World Cup during the past few months for personal reasons.
Ashton will name his 30-man squad next Tuesday with Strettle appearing to be a certainty for Ashton's elite World Cup group.
The 24-year-old made a try-scoring Test debut against Ireland during the RBS 6 Nations Championship last season, and he also started subsequent games against France and Wales.
He toured South Africa with England earlier this summer, but illness dashed his hopes of featuring in the two-Test series.
His latest setback is likely to ruin any chance he had of featuring in the World Cup.
England soccer stars David Beckham and Wayne Rooney both endured seven-week absences when they suffered similar injuries at various stages of their career.
Beckham broke the second metatarsal in his left foot 51 days before the 2002 World Cup, while Rooney broke the fourth metatarsal in his right foot prior to last year's World Cup.
A similar lay-off for Strettle would effectively sideline him throughout England's World Cup pool campaign between September 8 and 28.