Tippett landed awkwardly after taking a mark early in the game and was forced from the field, unable to take his kick.
The club initially feared Tippett had suffered bone damage, however, coach John Longmire revealed post match he has suffered ligament damage.
He will undergo scans over the weekend to determine the full extent of the injury and his likely time out of the game.
“There’s no break there so that’s a good sign, so they’re just looking at the ligament damage now,” Longmire said.
“(It was) obviously not ideal losing him so early, but the good thing is there’s no break there, from what I hear.”
The Swans could also be without midfielder Zak Joens next week, after he was placed on report for a late bump on Bulldogs’ forward Travis Cloke.