Rights activist Mohammadi, 52, who won the 2023 prize for her campaigning including against the death penalty, has been jailed since November 2021, and has spent much of the past decade in and out of prison.
The Paris-based family of Mohammadi emphasised it had no direct contact with her since her right to make phone calls was cut in November.
But it said it had learned from several other families of detainees held in Evin that clashes erupted on Tuesday as the female prisoners launched a protest in the yard against the executions.
According to rights groups, around 30 convicts were hanged this week, including Gholamreza (Reza) Rasaei, who the Iranian judiciary said was executed on Tuesday in connection with 2022 protests.
"The protest by prisoners against the execution of Reza Rasaei led to a violent crackdown by prison guards and security agents," Mohammadi's family said in a statement late Thursday, citing the reports.
"Several women who stood in front of the security forces were severely beaten. The confrontation escalated, resulting in physical injuries for some prisoners."
The family said that after being punched in the chest, Mohammadi suffered a respiratory attack and intense chest pain, causing her to collapse and faint on the ground in the prison yard.
She was bruised and treated in the prison infirmary but not transferred to a hospital outside, it said.
"We are deeply worried about her health and well-being under these circumstances," the family said.
Iran's prison authority denied that prisoners were beaten and blamed the confrontation on inmates.
Two prisoners "had heart palpitations due to the stress," but medical examinations determined that their general condition "is favourable," it said in a statement, according to the Tasnim news agency.
Relatives and supporters had earlier this month raised new concern about Mohammadi's condition, saying they had been informed of the results of medical tests carried out in July "which showed a worrying deterioration of her health".
In the past eight months, Mohammadi has been suffering from acute back and knee pain, including a herniated spinal disc. In 2021, a stent was placed on her main heart artery due to a blockage.
Mohammadi has kept campaigning even behind bars and strongly supported the protests that erupted across Iran following the September 2022 death in custody of Mahsa Amini, 22-year-old Iranian Kurd arrested for allegedly violating the Islamic republic's strict dress rules for women.
Mohammadi in June received a new one-year prison term for "propaganda against the state", on top of a litany of other verdicts that already amounted to 12 years and three months of imprisonment, 154 lashes, two years of exile and various social and political restrictions.
