The 26-year-old was initially ruled out for two months when it was discovered that he had damaged his medial ligaments following an awkward fall in the EFL Cup second-round clash with MK Dons a fortnight ago.
There had been fears that the injury was more serious that first thought, however, and Swansea have now discovered the full extent of the damage sustained by the Arsenal academy product.
"We were disappointed to lose Kyle. He has now had surgery and we expect him to be out for around 12 weeks," boss Paul Clement told the club's official website. "The period of 12 weeks is an estimate, and we will have to see how Kyle responds to his rehabilitation."
Bartley had recently broken into the Swans' first-team fold following his return from a successful loan spell with Leeds United last term.