"We have to search ourselves: have we done enough?" said the association's chair, Toralf Nilsson.
"The answer to this question must be no," Nilsson continued. "This gives an image of Swedish athletics that doesn't match the image we would like to give."
Aregawi has apologized, and SVT quotes the star runner as saying that she had gotten tablets earlier from a doctor in Ethiopia, and that she thought the tablets were vitamins. "It's my own fault that I took these tablets without checking," she wrote to the Swedish Athletic Association.
Stefan Olsson, the association's secretary general, reiterated that doping is "completely unacceptable within Swedish athletics."
Last month, Aregawi's A sample had tested positive for meldonium, a drug designed to treat low blood supply to body tissue that was added to the World Anti-Doping Agency's list of prohibited substances this year.
Aregawi is one of several athletes to have tested positive for traces of meldonium, including the Russian tennis star Maria Sharapova, Ukrainian biathlete Olga Abramova, and Russian cyclist Eduard Vorganov.
Doping expert: B-sample test unlikely to clear Aregawi6:09 min 6:09 min
Abeba Aregawi suspended over doping allegations1:13 min 1:13 min