The 22-year-old sustained the injury during a pre-tournament training camp in Portugal, with scans confirming that he has picked up a slight muscular strain.
The Bath back is expected to be sidelined for three to four weeks, which will see him miss both next weekend's match against France at Twickenham and the February 11 meeting with Wales at the Principality Stadium.
"It's disappointing news for Anthony and for England, but we know he'll rehab diligently to get himself right to go as soon as he can," head coach Eddie Jones told reporters.
"We're confident he'll be in the mix later in the championship."
Watson will stay with the England team to continue his rehab ahead of their title defence.