Season ticket holders can buy three extra tickets each for the match against Doncaster Rovers at Wembley.
The rush for tickets was causing traffic problems on the A643 at Elland Road on Wednesday.
The club said no more fans should go to the ground. Leeds have been allocated a total of 36,000 seats for the match.
Tickets, if any are remaining, go on general sale to the public on Thursday.
A statement on the club's website said: "Fans were arriving at Elland Road late on Tuesday afternoon to begin queuing ahead of the opening of the ticket office on Wednesday. There are extremely long queues at the ticket office and the club is advising further fans not to arrive at Elland Road."