The English Rugby Football Union confirmed on Sunday that Mitchell will miss the Calcutta Cup showdown at Murrayfield, with no date set for his return.
Harry Randall has been named as the replacement in Steve Borthwick's 36-man training squad.
Danny Care and Ben Spencer are competing to fill the void left by Mitchell in the number nine jersey.
Mitchell has established himself as England's first-choice scrum-half since forcing his way into the squad for last year's World Cup despite being dropped early in the build-up campaign.
He started the semi-final loss to South Africa and retained Borthwick's approval for the victories over Italy and Wales that have opened the Six Nations.
Centre Ollie Lawrence, who sat out the first two rounds of the Six Nations because of a hip injury, has been passed fit to resume full training this week.
Lawrence has been missing since late January with a problem sustained with his club Bath.
Borthwick names his team on Thursday as England look to stop a run of three successive defeats against old rivals Scotland.