Cort has been limited to just three Championship starts for Burnley this season with his run of games in October being ended by a red card against Reading.
The former Hull and Stoke City central defender, 31, moves to Deepdale until the end of December to help Preston’s bid to climb away from the foot of the Championship table.
Burnley boss Brian Laws explained: “Leon is disappointed he’s not in the side after he lost his position after being sent off for the first time in his career.
“But it’s not just that that’s cost him, it’s his position at the moment. Michael Duff has come in and formed a good partnership with Clarke Carlisle.
“And when you are an experienced player you want to play and this has come at a good time for him and a good time for us because Andre Bikey is also fully fit, ready to go and desperately wants to play.
“That just helped the fact that I think it would be a good time to let Leon go out on loan for a month to get some games in that period and then we can call him back if and when we need to.”
Cort, who signed for Burnley from Stoke in January, becomes the fifth player currently out on loan from Turf Moor, following Kevin McDonald, Richard Eckersley, Wes Fletcher and Kevin Long.