The Prosecutor General's Office said in a press release that the 12 suspects had been detained in the districts of Vilnius, Kaunas and Vilkaviskis, and in Klaipeda and other cities, and had their homes searched.
They were released after signing a written undertaking not to leave their place of residence.
Twenty-six persons, including two MPs, have been recognized as victims in the investigation.
The probe covers three articles of the Criminal Code: on riots, unlawful collection of information about a person's private life, and unlawful possession of narcotic or psychotropic substances for the purpose other than distribution, according to the press release.
Some 5,000 people gathered outside the parliament building on August 10 to protest against the government's plans to impose restrictions for those who refuse to get vaccinated or tested for COVID-19.
The rally turned violent in the evening, with some protested blocking exits from the parliament and throwing bottles and flares at police officers. The police used teargas against protesters.