The 31-year-old midfielder is suspected of "committing the criminal offence of giving false testimony" on June 13.
The 31-year-old midfielder is suspected of "committing the criminal offence of giving false testimony" on June 13 at the tribunal in eastern Croatia, according to the prosecutors' statement.
The statement did not name Modric directly but referred to "a Croatian citizen born in 1985".
Mamic is accused -- along with his brother Zoran Mamic and two others -- of abuse of power and graft that cost the former Croatian champions more than 15 million euros ($17.6 million), and the state 1.5 million euros.
Cash was allegedly embezzled through fictitious deals related to player transfers, and Modric was called last week to testify over the details of his 2008 transfer from Dinamo to Tottenham Hotspur.
From there he joined Real Madrid in 2012.
The prosecutors alleged that, when questioned last week, Modric falsely said he had signed an annex to a contract with Dinamo over conditions for future transfers in July 2004.
When questioned during investigations in 2015, Modric said the annex was signed after he joined Tottenham, according to the prosecutors.
False testimony is punishable with up to five years in jail.
Modric was visibly uncomfortable and at times appeared confused last Tuesday when he gave evidence at the tribunal.
The trial has attracted huge interest from media and residents of Osijek where it is being held, reportedly to avoid Mamic's influence on judges in the capital Zagreb.
Mamic is considered the most powerful man in Croatian football and his connections extend into many spheres of public life.
Most Croatian football fans see him as the real boss of the Croatian Football Federation and believe its formal chief Davor Suker is merely Mamic's puppet.
Since the trial opened in April under strict security, Mamic has lived up to his controversial reputation, easily losing his temper and trying to turn the process into a performance.
His angry outbursts on Wednesday, when Liverpool defender Dejan Lovren was due to give evidence, led to the trial being adjourned until July and Lovren's testimony postponed until September.
Modric, who grew up as a refugee child in Zadar on the Dalmatian coast, is highly popular in Croatia where he has a reputation for modesty.
He was only six when Croatia's independence war broke out, and although Zadar was heavily bombed his football skills in the corridors of a refugee hotel and in cratered car parks did not go unnoticed.