The 24-year-old, who has scored 15 tries in 33 tests for his country, left the field on an electric cart after 34 minutes of Saturday's 24-15 Six Nations defeat by Ireland at Twickenham.
British media said he would be sidelined for about six months, ruling him out of England's tour of South Africa in June. He will also be missing for Bath's last five games in the Premiership run-in as they try to make the playoffs.
"Anthony has been in superb form this year, and we’re obviously really disappointed to have lost him at a critical part of the season," Bath's Director of Rugby, Todd Blackadder said on the club's website (www.bathrugby.com).
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England are already set to be without Courtney Lawes and Nathan Hughes for the three-match series against South Africa after both players had knee surgery last week.
(Writing by Ken Ferris; Editing by Nick Mulvenney)
