State television said Mamic was arrested over 80-million-kuna (7 million pounds) worth of damage suffered by the club related to suspect player transfers.
A police source confirmed the reason for the arrest and said several other people were also detained. State TV said four other people were held.
Mamic's lawyer declined to comment on the matter.
Dinamo Zagreb said on its website that an anti-corruption police unit had entered the club premises early on Wednesday.
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The Croatian soccer federation (HNS) said on its website that police had also raided its premises.
State news agency Hina reported that HNS's Chief Executive and former Dinamo official Damir Vrbanovic had been arrested at Zagreb airport as he returned from Russia where Croatia played a friendly on Tuesday.
Neither the HNS spokesperson nor Vrbanovic's lawyer were immediately reachable for comment.
Zdravko Mamic and his brother Zoran, who is Dinamo's coach, were previously detained in July for questioning over embezzlement and tax evasion, before being released.
(Reporting by Igor Ilic; Editing by Janet Lawrence)
