Dortmund face German rivals Bayern Munich at Wembley on May 25.
The finalists have been allocated 50,000 tickets between them for the Final, even though the total capacity at the stadium will be 86,000.
Prices for the match will start at £60 per ticket (R840) and go up to £330 for the top category, meaning German fans could end up paying more for a ticket than they do for a Bundesliga season ticket.
In the 24 hours after they triumphed over Real Madrid in the semi-finals last Tuesday, more than 250,000 requests were sent to Dortmund for Final tickets.
The club will hold a ballot to determine which of the 502,567 applicants will be successful.
“10 years ago every member of our club would have had a chance for a ticket,” club chairman Hans-Joachim Watzke said.
“Since we only have 24,000 at our disposal, we will only be able to fulfil every 20th request.”
Watzke points to the “rapid growth” of the club's fanbase, saying Dortmund have almost 100,000 members compared to 8,000 around a decade ago.
Borussia reached their only previous final in 1997 when they beat Juventus 3-1.