Geraghty, a fly-half or centre who made his Test debut during last season's RBS 6 Nations Championship, will undergo an MRI scan later on Monday.
Part of England's 31-man training squad preparing to meet France in Paris next Saturday, Geraghty had been tipped to make the match-day 22.
Geraghty, 21, went off just before half-time at the Madejski Stadium.
He was then assessed by England's medical team and it was clear he could not be considered for the trip to Paris.
Geraghty made his Test debut against France at Twickenham last term, and he has been in a rich vein of form recently, including a man-of-the-match display for England Saxons against Ireland A earlier this month.
England head coach Brian Ashton is due to name his starting line-up on Tuesday afternoon for the France clash.
Changes are expected following the unimpressive 23-19 victory over Italy last time out.
Wing Paul Sackey (thumb), centre Jamie Noon (hamstring) and lock Steve Borthwick (knee) though, who all sat out their clubs' Premiership games on the weekend, look as though they will be available for selection.
England must beat Les Bleus to keep alive any chance of capturing the Six Nations title, but France are currently top on points difference from Wales after beating Scotland and Ireland in their opening two fixtures.