The striker suffered ligament damage on Saturday during the team's 1-0 win over Middlesbrough in the Championship.
Doukara joined Leeds on a season-long loan from Catania last month.
"Souleymane has ruptured his ankle ligaments. He was involved in a really bad tackle against Middlesbrough right on half time," Hockaday told the club's official website.
"It won't just be for one or two weeks, he will be out for a number of weeks. We'll need to see how it settles down but I think it will be three or four weeks minimum."
Leeds are back in action on Saturday when they travel to Watford in the Championship.