Rehesabz.net said the incident happened in the northern city of Zanjan after authorities reportedly banned most memorial services for Montazeri, who died aged 87 on Saturday, after his funeral turned into an opposition rally.
"People gathered for Ayatollah Montazeri's memorial were faced with locked mosque doors and decided to hold the ceremony in the street," Rahesabz.net said.
"People were mourning in silence and the Koran was being recited but the police sought to disperse them which led to clashes and people were severely beaten as they were running away.
"Many have been arrested and some of the injured have been taken to hospital," the website added.
The report could not be independently verified as AFP and other foreign media are banned from covering opposition-linked gatherings.
Montazeri was an inspiration to reformists and human rights activists in Iran and came out in bold support of the opposition movement challenging the disputed June re-election of President Mahmoud Ahmadinejad.
Parlemannews.ir, the website of the reformist minority faction in parliament, said Thursday it had learned of a ban on most services for Montazeri after security officials prevented a mosque ceremony in the town of Kashan in Isfahan province on Wednesday.
"Security officials warned the organisers and hung a banner in front of the mosque which read: 'At the order of the supreme national security council, holding any ceremonies across Iran for Mr Montazeri is banned, except in Qom and Najafabad,'" it said.
Parlemannews and some opposition websites also carried a picture of the banner.
Iranian authorities did not immediately comment on the reports.
Montazeri was based in the shrine city of Qom and hailed from Najafabad in Isfahan province, where he had many followers.
Security forces prevented mourners from holding a memorial service for the cleric in Isfahan city on Wednesday and more than 50 people were reportedly arrested after heavy clashes.
Hundreds of thousands poured into the streets of Qom for Montazeri's funeral on Monday, effectively turning the ceremony into an opposition rally.
The cleric's family has reportedly cancelled the memorial service for Montazeri on Saturday which Iranians traditionally hold on the seventh day after someone's death.
Montazeri's seventh day of passing falls on the day before Ashura, which is a major Shiite mourning festival.
Police have vowed to crack down on any protests during this period.
Montazeri was once tipped to succeed the founder of the Islamic revolution Ayatollah Ruhollah Khomeini but fell from grace in the late 1980s after criticising the regime's treatment of its opponents and political prisoners.
