The club were expecting to sell out their 33,000 allocation today and postal applications, from members who qualify for tickets, were also being processed.
Leeds had over 4,000 postal requests from members and were aiming to despatch them by mail tomorrow.
However, there are no tickets left for supporters who hold a ticket stub from the play-off semi-final first leg against Preston and there will be none available for general sale.
Chief executive officer Shaun Harvey says in the Yorkshire Evening Post: "Every single season ticket holder who applied has got their tickets and those remaining were available to members today.
"It's unlikely that there will be any tickets left after today's sales and it would be unfair to invite supporters to attend tomorrow without any chance of success."
The ticket office will now be closed tomorrow to prevent supporters making a wasted trip.
The club's ticket office line – 0845 121 1992 – will be in use again from tomorrow.