The Swedish FA's disciplinary committee said that even if it was not clear where the firework came from the subsequent behaviour of the AIK fans meant the April 25 game could not be restarted.
Syrianska had just taken a 1-0 lead when AIK had forward Teteh Bangura sent off for stamping on the home keeper. Several firecrackers were then thrown from the stands on to the pitch.
In a statement on the SvFF website the committee said it reviewed video evidence and submissions from both clubs and the match officials.
Following the investigation, the committee laid the blame on AIK supporters who threw fireworks at ball boys and Syrianska fans in an adjoining section after the match was stopped.
"Throwing firecrackers towards people in this way has to be seen as being particularly ruthless, and creates a significant threat of personal injury," said the statement.
"AIK bear strict responsibility for this and therefore shall be subject to sanction."
AIK's punishment for the match being abandoned after 20 minutes was Syrianska being awarded the points with the fine imposed on AIK for the firecrackers thrown at the ballboys.
AIK, who have until May 26 to appeal, stay seventh with 11 points from seven games while Syrianska are now fourth from bottom of the 16-team standings with five points.
AIK are one of several Swedish clubs whose games have recently been disrupted by the unauthorised use of fireworks.
A female fan was injured during the derby between Gothenburg and GAIS while the Stockholm clash between local teams Djurgarden and AIK had to be stopped several times.
The problem has led the SvFF to ban pyrotechnics inside stadiums and instruct referees to halt play immediately if they see fireworks being used in the stands.