Briefs have been for sale to season ticket holders and this season's match attendees only thus far, with a general sale due to start on Monday, March 10.
But with tickets flying out of the Pittodrie ticket office as fast as they can print them, the club will reach its allocation before then.
However AFC is doing all it can to secure extra matchday permits before the final with Inverness on March 16.
Fans who haven't attended a match so far this season can secure a final brief by heading to watch the Dons play Dumbarton in the Scottish Cup on Saturday.
An AFC spokesperson said: "With the team welcoming Dumbarton to Pittodrie on Saturday (KO 3pm), there is still time for supporters to create a buying history and secure Cup Final tickets now.
"Please note, you must purchase your tickets for this match in advance from the Ticket Office in order to complete your buying history.
"Ticket sales for the Cup Final will stop between 2-3pm on Saturday to allow us to process sales for the Dumbarton match. Sales will resume via the Ticket Office after the match."
League Cup final tickets are £25 a pop, and a tenner for under-16s.