The test for banned substances was conducted by the International Association of Athletics Federations (IAAF).
“It is with dismay and with extreme disappointment that we report this issue,” said SFIF general secretary Stefan Olsson.
“We totally reject all forms of cheating, doping…We have a zero tolerance, and this is totally unacceptable,” he said.
A full investigation will now be conducted, according to the association.
“Because this is an ongoing investigation, we cannot disclose the actual substance that she tested positive for,” Fredrik Trahn, an association spokesman, told the AFP news agency.
“She is provisionally suspended, effective immediately.”
But Swedish tabloid Aftonbladet reported that SFIF's medical expert, Åke Andrén-Sandberg, had confirmed that Aregawi had tested positive for meldonium, a substance which was banned in sports at the start of 2016, just before her doping test.
The 25-year-old athlete, who competed for Ethiopia at the London 2012 Olympics, was world champion in 2013 in Moscow, but finished only sixth in a slow tactical race in Beijing last year.
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She has also won the European championships and World Indoors gold over her specialist distance.
She finished fifth at the London Games, again in a slow tactical race, behind Turkey's Asli Cakir Alptekin, who was later stripped of her Olympic title for a second doping offence.
But Aregawi switched allegiances to Sweden soon after the last Olympics, gaining citizenship through her marriage to a naturalized Swede of Ethiopian origin.