Modric is alleged to have given a "false testimony" in June 2017 when authorities were investigating his 2008 transfer from Dinamo to Tottenham.
Mamic and three others are accused of corruption, having allegedly taken a cut from player sales, ultimately costing Dinamo and the state.
A crucial part of Modric's situation relates to when he signed an annex to his Dinamo contract, which detailed the terms of the deal and a 50-50 split of any transfer fee he would later generate.
According to prosecutors, Modric revealed to authorities in 2015 that the annex had been signed after his move to Tottenham.
But Modric, who could face up to five years in prison if found guilty, then changed his testimony, claiming it had been signed in 2004, with prosecutors alleging this was done to favour Mamic.
The attorney's office insist Modric was warned by the judge in June "that he was obliged to tell the truth and that giving false testimony is a criminal offence" upon bringing the charge against him on Friday.
However, the Croatian Football Association (HNS) is "deeply convinced" of Modric's innocence and "stands firmly" with the captain of the senior national team.
Their statement read: "The Croatian Football Association always and consistently supports the principle of presumption of innocence and considers every person innocent until proven otherwise.
"In a specific procedure, HNS is deeply convinced of the correctness of Luka Modric's testimony before the court in Osijek, and especially because of Modric's behaviour since his first appearance for the Croatian U-15 team in March 2001 to date.
"In almost 20 years, Modric has shown himself as a character… who is extremely responsible in his relationship with team-mates, obligations to the national team and the Croatian state, whose play in the national team and clubs has played a significant role in the sporting world.
"Thanks to his immaculate sports career and behaviour in the team, in 2016 he became the captain… and in international clubs he was confirmed as the most successful Croatian football player in history.
"Because of all this, the Croatian Football Association stands firmly with its captain of the team and believes that this process will confirm his innocence, as well as the unfoundedness of this indictment.
"We are also convinced that, thanks to Modric's unbeatable character, this process will not have a negative impact on the performance of the national team… at the FIFA World Cup in Russia."