Edelman sustained the injury in a preseason game on Aug. 25, with his surgery coming just over four weeks later.
The short video on Wednesday showed Edelman running with cords as Drake's song entitled "God's Plan" was heard in the background. He also posted the word "Determined" in the comments section.
Edelman said earlier this month in an interview with Barstool Radio that he's progressing.
"You never want to put a number on anything," Edelman said. "You put a number on something, you're feeling great this day [but] you go out and the next day, something swells up, this, that, and then who's fault is that? Is it the trainer's fault? Is it the player's fault? Is it the doctor's fault? You just say 'We're trying to get better each day.'"
Edelman had a step on Detroit Lions linebacker Jarrad Davis and caught the ball at Detroit's 29-yard line before turning up the field in the preseason game. He planted his right foot into the turf before immediately reaching for the back of his right knee.
The 31-year-old Edelman has recorded 425 receptions for 4,540 yards and 24 touchdowns in 103 career games since being selected in the seventh round by the Patriots in the 2009 NFL Draft.