Kennedy, who is one of the leading contenders for the Brownlow Medal, was given the red vest at quarter-time and replaced by Dean Towers.
The midfielder looked a dejected figure in the back row of the Swans' interchange area, as the club's medical staff worked on the injury.
No details were immediately available from the Swans.
Kennedy has proved one of the game's most enduring players, having played 126 consecutive matches.
The 26-year-old had seven touches in the first quarter.
