The national competition authority, GVH, announced the fine, which is equivalent to around €40,000, along with a smaller fine of HUF3 million (€12,000) for struggling Parmalat brand KYR, on similar charges.
Danone had advertised its Activia yoghurt range as a "rich source of protein, vitamins, calcium and phosphorous" but this claim was subsequently rejected as unfounded by Hungary's National Food and Dietetic Institute.
Blandine Ruty, communications manager at Danone, said the company had received little information on the GVH investigation and would await written confirmation before taking any action.
"They [GVH] are questioning the scientific legitimacy of the claim, that's all we know. They haven't contacted us to ask us to change anything, but we are open to do that if there is a problem," said Ruty, who was frustrated at the lack of communication from the GVH.
A spokeperson for GVH said that the authority could give no more details until written confirmation of the decision had been sent to the companies involved.
The announcement is nevertheless embarrassing for Danone, which is currently the market leader in fresh dairy products across Eastern Europe with total dairy product sales there of €0.9 billion.
Peter Sukosd, also of the GVH, said that the authority's policy was that if any company claimed its product was better than its rivals on the market, then it had to show proof.
And Danone and Parmalat are not the first big dairy companies GVH has had to deal with. German company Zott has been in trouble with the competition watchdog three times over the last couple of years.
In one case, Zott was also fined HUF10 million (€40,000) for misleading consumers after its advert for Zott Monte chocolate and hazelnut flavoured milk dessert claimed that "Zott Monte is the most advisable for your children".
Sukosd was unable to give further details because Zott has chosen to appeal against the GVH decision to the Metropolitan Court.