The Harlequins player picked up the injury in England's 27-22 defeat by reigning champions Ireland in Dublin at the weekend, in which he scored a try on debut.
He has been replaced in Steve Borthwick's squad by Saracens centre Alex Lozowski (31), the Rugby Football Union announced on Tuesday.
Lozowski won the last of his five international caps under former head coach Eddie Jones in 2018.
If Murley recovers quickly he could be available for fixtures against Italy and Wales later in the Six Nations.
Ollie Sleightholme, Tom Roebuck and Elliot Daly are the contenders to fill the number 11 jersey when Borthwick names his team on Thursday.
Defeat in Ireland was a sixth loss in seven matches for Borthwick's side.
France hammered Wales 43-0 in their opening Six Nations fixture.