The 19-year-old paddler had been due to contest the C2M 1000m with brother Oleg, but will now no longer be eligible, the ICF said.
It was unclear whether Tarnovschi would be stripped of his medal.
ICF Secretary General Simon Toulson told Reuters the status of Tarnovschi's medal would be determined by an International Olympic Committee-led hearing.
He did not know when it would take place but said it would be "as soon as possible".
The test uncovered an "atypical finding", Toulson said, and occurred prior to any Olympic events.
Toulson has not spoken to Tarnovschi but said the Moldovan National Olympic Committee was "obviously asking a bunch of questions to us".
"I don't think they've got much experience in this," he said.
IMAGE: Bronze medallist Serghei Tarnovschi of Moldova celebrates on the podium during the men's Canoe Single 1000m Final A on Day 11 of the Rio 2016 Olympic Games on August 16, 2016.
Photograph: Buda Mendes/Getty Images
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