Mutu, sacked by English Premier League club Chelsea in 2004 after using cocaine, gave a positive sample on January 10 at the Serie A game between the Florence club and Bari.
"In the first sample analysed, the presence of a metabolite of sibutramine has been revealed for Adrian Mutu," the statement said.
CONI, which acts as Italy's anti-doping body, gave no further details but has a long track record of pursuing bans for sportsmen and women who fail tests - even if they took drugs by accident.
However, CONI did absolve Italy captain Fabio Cannavaro last year when documentation was not filed correctly by Juventus after he received emergency treatment for a wasp sting.
Mutu has had a truncated season with Fiorentina, partly because of injury and partly because of the continued fallout from his 2004 sacking by Chelsea.
The English club wanted compensation and football authorities and the Court of Arbitration for Sport backed their claim, asking the 31-year-old former Parma and Juventus forward to pay over 17 million euros.
Mutu appealed again to a Swiss federal court and the situation is now on hold, although Fiorentina coach Cesare Prandelli has acknowledged the saga was playing on Mutu's mind and he has not always picked the forward this season.
Fiorentina, who qualified for the Champions League group stages but have slipped to ninth in Serie A after a poor run of form, said they would not tolerate drug use but would stand by Mutu until further proof was provided.
"Fiorentina, which confirms it is against the use of any banned drug but believes in the good faith of the player, will try to clear up the situation as soon as possible," a club statement said.
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