"It looks like he's definitely going to miss some time," Maple Leafs head coach Sheldon Keefe said following his team's 3-1 loss, according to Sportsnet's Chris Johnston.
Keefe added that more tests are required to determine the extent of the injury, according to TSN's Kristen Shilton.
Thornton appeared to jam his wrist while absorbing a hit from Oilers forward Josh Archibald along the boards early in the third period.
The collision occurred less than two minutes into the final frame. Thornton left for the dressing room shortly thereafter and didn't take another shift.
Thornton has one goal and one assist in five games with his new club after signing a one-year contract in the offseason. The 41-year-old collected both of his points in a victory over the Ottawa Senators on Saturday.