FIFA transfer rules ban players and clubs from making payments to intermediaries for under-age players.
"It has been clarified that AIK paid compensation to an intermediary in connection with Alexander Isak's transfer to Borussia Dortmund. As Alexander Isak was under 18, this is forbidden," the SvFF Disciplinary Committee said in a statement.
Isak was courted by top clubs from all over Europe before joining German club Dortmund in January for a reported fee of 10 million euros.
AIK have until May 16 to appeal against the decision.
(Reporting by Philip O'Connor, editing by Ed Osmond)