After the game, Haley told reporters the "initial signs on extremities were positive", according to Josh Looney of KCChiefs.com.
Leggett will stay in Tampa overnight.
He was trying to tackle Bucs running back Kareem Huggins when he went to the ground.
Trainers came out and tended to him for 10-15 minutes before a cart came onto the field. He was put onto a stretcher and carried off.
The Chiefs and Bucs sidelines both had come onto the field. The Chiefs huddled in a team prayer at one point.