The 26-year-old former Arsenal defender damaged his knee after failing badly in the 4-1 League Cup win over MK Dons in August.
He was stretched off the field on that day, and has now come through a successful operation.
Bartley, who spent last season on loan with Leeds United, returned this term to force his way into the Swans first team.
And manager Paul Clement says it is a blow to lose his defender at this stage in the season.
He told the club’s official website: “We were disappointed to lose Kyle. He has now had surgery and we expect him to be out for around 12 weeks.
“The period of 12 weeks is an estimate, and we will have to see how Kyle responds to his rehabilitation.”