Five-time major champion Sharapova said the change in WADA's banned list for 2016 led to an inadvertent violation, for which she will be "provisionally suspended."
Sharapova said she had been taking meldonium for ten years for health reasons.
The founder of meldonium suggested that the drug would not help boost performance.
Former world champion Aregawi joins an ever-growing list of sportspeople to have tested positive for the drug this year, others include the 2015 Tokyo marathon champion Endeshaw Negesse, Ukrainian biathletes Olga Abramova and Artem Tyschcenko, as well as Russian ice dancer Ekaterina Bobrova.
"Two samples were taken, an A and a B sample. The A sample had already come back positive, and is usually the case when that happens, the B sample has now also come back positive," said Tommy Forsgren, the doping manager for the Swedish Athletic Association.
"Unfortunately, we're not surprised."
Aregawi, a 1500m specialist, now risks a suspension of up to four years.
She assumed responsibility for the doping on Wednesday.
"I previously received pills from a doctor in Ethiopia. I thought they were vitamins. It's my own fault that I took these pills without checking," Arewagi said in a statement released by the Swedish Athletic Association.
She also won the European Championships and the World Indoors titles over her favourite distance.
Aregawi switched allegiances to Sweden soon after the Olympics, through her marriage to a naturalised Swede of Ethiopian origin, of which she was accused of doing just to gain citizenship.
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