The Welsh international has been a part of Simon Grayson's plans since joining Leeds in early September, playing in four first-team fixtures and making regular appearances on the bench, but the recovery of Shane Higgs from a minor hamstring strain has removed the need for additional cover for first-choice Kasper Schmeichel.
Higgs was not included in Saturday's 18-man squad but he proved his fitness in a friendly against Liverpool last week and Grayson said he could not justify the "luxury" of having three experienced options at Elland Road.
Grayson said: "Jason will go back to Blackburn now. I'd like to thank him for what he's done because he's been good in the dressing room and good when he's come into the team but Shane Higgs is back fit and we can't have the luxury of having three good goalkeepers on our books."
Brown's signing was made necessary by a foot injury suffered by Schmeichel in the last week of August and Blackburn were willing to release a player whose involvement at Ewood Park has been fleeting.
The 28-year-old warned Rovers in the summer that he intended to seek new employers and had spoken positively about the possibility of joining Leeds permanently.
Higgs was planning to complete a full week of training prior to reclaiming a place on the bench at Norwich City this weekend but United's squad has been temporarily diminished with three players departing for international duty.
Davide Somma, George McCartney and Max Gradel were called up last week by South Africa, Northern Ireland and the Ivory Coast respectively and Somma and Gradel are hoping to make their debuts in friendlies on Wednesday night.
All three are due to return in time to feature in Saturday's Championship fixture at Carrow Road.