The Croatian champions announced Mamic's departure late Monday as the club prepare to face Tottenham in Thursday's Europa League last 16 return leg. Spurs lead 2-0 after last week's first leg in London.
Mamic's exit came after the Supreme Court upheld a 2018 ruling by a local tribunal but reduced his initial prison sentence by three months.
"Although I do not feel guilty, as I said earlier if the verdict becomes final I will accept it and quit as Dinamo coach and sports director," Mamic said in a statement.
Assistant coach Damir Krznar will replace Mamic as both manager and sports director.
In 2018, Mamic, his brother and former Dinamo Zagreb boss Zdravko Mamic, a former club director and a tax inspector were all found guilty of graft which, according to the indictment, cost Dinamo more than 15 million euros ($18 million) and the state 1.5 million euros.
The cash was embezzled through fictitious deals related to player transfers, notably two international stars -- Real Madrid midfielder Modric and defender Dejan Lovren.
They both appeared as witnesses during the trial providing details of their transfers from Dinamo.
At the time Zdravko Mamic was sentenced to six years and six months in jail and the Supreme Court upheld his verdict.
He fled to neighbouring Bosnia just ahead of the verdict.
Earlier this month another trial involving the Mamic brothers and three others embezzling millions of euros from Dinamo Zagreb opened before a local tribunal.
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