With number one Kasper Schmeichel picking up a foot injury, manager Simon Grayson has opted to bring in some cover.
Shane Higgs has now started two of Leeds' last three outings, including Saturday's 2-1 Championship success over Swansea at Elland Road.
With Schmeichel set to miss their upcoming games with Barnsley and Doncaster, Grayson has brought in Brown.
Brown was on the bench for the visit of Swansea and is likely to stay there until Schmeichel recovers from his foot injury.
"Kasper picked up a foot injury a couple of weeks ago and we are assessing him as we go," he told the club's official website.
"We have a lot of games coming up and I am delighted Jason has agreed to come in."