Faezeh Hashemi, the daughter of former Iranian president Akbar Hashemi Rafsanjani
Hashemi was arrested in the capital Tehran on September 27 for encouraging residents to demonstrate amid nationwide protests sparked by Mahsa Amini's death.
"My client, Ms Hashemi, was sentenced to five years in prison by the preliminary court," her lawyer Neda Shams said, adding she plans to appeal the verdict.
The 60-year-old former lawmaker and women's rights activist was charged with "collusion against national security, propaganda against the Islamic republic and disturbing public order by participating in illegal gatherings", the lawyer said.
"The decision, which is not final, was communicated to me on Wednesday, and we will appeal it within the time frame allowed by law," added Shams.
Hashemi has faced similar charges before, and in 2012 was arrested and sentenced to six months in prison for "propaganda against the Islamic republic".
Last October, judiciary spokesman Massoud Setayeshi said without elaborating she had been sentenced in March "to 15 months in prison and two years of additional punishment including the prohibition of activities on the internet".
Hashemi's late father, president between 1989 and 1997 who died in 2017, was considered a moderate and advocated improved ties with the West.
Iranian authorities say hundreds of people, including members of the security forces, have been killed and thousands arrested in connection with the protests, which they generally describe as "riots".
Four people have been executed, and the judiciary has said 13 others have been sentenced to death over the unrest. Six of these defendants have been granted retrials.