Curry picked up the injury in Sale's 21-13 Premiership semi-final win over Leicester Tigers on Sunday and will miss the final against Saracens at Twickenham this Saturday, the club said.
"Gutted that my season is over like this but looking forward to supporting the lads over the next two weeks," Curry said on Instagram.
Neither the club nor Curry mentioned a date for his return, though The Times reported he is likely to be out for at least four months.
His identical twin Tom also plays for England and started in the 2019 World Cup final, where they lost to South Africa.
England, 2003 World Cup winners and runners-up at the last edition in 2019, begin their campaign in France on September 9th against Argentina. Their Pool D opponents also include Japan, Samoa and Chile.
