Chelsea were initially willing to allow United 3,000 tickets for the clash, but the London Borough of Hammersmith and Fulham has stepped in and amended the club's safety certificate.
Over 8,000 fans had applied for tickets and managing director David Richmond apologised to the many disappointed die-hard supporters.
Richmond said: "We've fought tooth and nail to get the full allocation, but there is nothing either us or Chelsea can do about it. We've been to the highest authority in the hope of securing the tickets we want, but no one has the power to veto the decision.
"Our supporters have been tremendous this season, particularly away from home, and this is a major disappointment. We wanted them to be there in massive numbers."
The decision has also caused problems for the supporters club as spokesman Ray Fell said: "There are a lot of disappointed people. Leeds fans have traditionally been good for a long time now. To be punished for what could be our last game in the Premiership after the fans have fought like hell to keep Leeds up is a big blow."