The semi-official Fars News Agency, which did not identify the detainees who are to be put on trial, said one was accused of moharebeh -- an Islamic term meaning waging war against God -- which carries the death sentence.
The others were accused of gathering with the intention of disrupting national security and propaganda activities against the Islamic establishment, Fars said.
Eight people were killed in clashes between security forces and supporters of opposition leader Mirhossein Mousavi on Ashura, the day of ritual Shi'ite mourning that fell on December 27.
It was the most serious violence since the aftermath of a disputed presidential election in June, which the pro-reform opposition says was rigged, a charge the authorities reject.
The opposition website Rahesabz said earlier this month that more than 180 people, including 17 journalists, 10 Mousavi aides and some members of the outlawed Baha'i faith, were arrested after the Ashura day demonstrations.
Hardline clerics and authorities have called on the judiciary to punish opposition leaders for creating tension in Iran, saying they were mohareb (enemies of God).
The files of 16 of the accused arrested on Ashura have been sent to Tehran's Revolutionary Court for consideration, Fars said, citing a court statement. All the 16 are in detention. Their trial will begin soon, Fars added.
Last week, the official IRNA news agency said five detainees that Iran planned to put on trial in connection with the Ashura day protests were members of the armed People's Mujahideen Organization of Iran (PMOI).
The PMOI is an exile group opposed to the Islamic system of government. Friday's Fars report did not make clear whether any alleged PMOI members are among the 16 to be tried soon.
The June election plunged Iran into its biggest internal crisis since the 1979 Islamic revolution and exposed deepening divisions within the establishment. Despite many arrests and the authorities' crackdown, street protests have continued.
(Writing by Fredrik Dahl; editing by Paul Taylor)