Police say alleged fraud has cost the club 118m kunas ($17.3m, £11.1m) since 2008.
The brothers say they are determined to prove their innocence.
On Friday, anti-corruption investigators said a senior official with the Croatian Football Federation, a tax inspector and the Mamic brothers were suspected of giving bribes, tax evasion and other offences.
According to Croatian and German media reports, they are accused of taking a cut of the sales of Dinamo Zagreb players.
Police allege the fraud also cost the state 12m kunas ($1.8m, £1.1m).
Police searched offices at the club and the football federation, as well as the brothers` homes, on Thursday. Two other men were also detained.
Officers are keen to keep the four suspects in custody, but a court in Zagreb has yet to rule whether they will continue to be held.
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