The 30-year-old was stretched off after colliding with Toffees goalkeeper Tim Howard and left Goodison Park on crutches while wearing a protective support on his leg.
Seasiders boss Ian Holloway, who is also set to be without Alex Baptiste after the full-back needed stitches in a leg wound picked up at the weekend, is awaiting the results of a scan on Taylor-Fletcher with trepidation.
"You always fear the worse when one of your lads get injured," he told the Blackpool Gazette. "Fletch's kneecap and thigh were going one way and the lower part of his leg was knocked back the other way - that normally means some ligament damage.
"Fletch's knee is badly swollen and very sore. He has a cast on it and when it settles down we will see how he is. I have never seen anything like it in my life."
Holloway hopes to have Matt Phillips back in contention following the winger's two-match absence with a hamstring problem.