The two-time Lions tourist suffered a torn calf in Saturday's 17-9 win over France and faces approximately four weeks on the sidelines.
The 31-year-old, who missed the win over Italy a fortnight earlier with a back injury, left the field before half-time and was again replaced by Alex Corbisiero.
The news will be a major blow to Martin Johnson's plans. England are so far unbeaten in the Championship and face Scotland and Ireland in the final rounds as they chase the Six Nations crown and Grand Slam glory for the first time since 2003.
Corbisiero is likely to fill the void left by Sheridan after impressing against strong Italy and France front rows.