Dortmund, who have an average home attendance of around 80,000, said 502,567 fans had applied for tickets online before Sunday's deadline.
"It's absolutely crazy," said the club, adding that a draw would be made to determine who would get the 24,042 tickets the club has been allocated for the match on May 25.
The two finalists have been allocated 50,000 tickets for the final at London's Wembley Stadium, even though the total capacity will be 86,000.
Prices start at £60 per ticket and go up to £330 for the top category, a shock for German fans used to much lower prices for Bundesliga matches.
Fans could end up paying more for a ticket for the Wembley final than they do for a season ticket at home in Germany where modern stadiums have low-cost standing areas.
Dortmund reached their only previous final in 1997 when they beat Juventus 3-1.