The move comes after Montazeri on Monday called on leading Shiite clerics to end their silence over a crackdown on massive street demonstrations that followed disputed June presidential polls.
The opposition, which has alleged widescale fraud and has refused to recognise President Mahmoud Ahmadinejad's re-election, has called for continued protests.
"My three sons were arrested on Monday by people who came to our door with a warrant issued by the Special Court for Clergy in Qom," the cleric's son Ahmad Montazeri was quoted as saying by the reformist Etemad newspaper.
He said that the children of Ayatollah Hossein Mousavi Tabrizi, who heads a pro-reform group of Qom scholars, have also been arrested, as well as another member of the group, identified only as Ayatollah Nazem.
The young men detained are in their 20s, Montazeri said.
Reports said Nazem is also close to the elder Montazeri, who has been a vocal critic of the Islamic republic's authorities, especially concerning their handling of Iran's June 12 election and its aftermath.
The opposition plans to pour on to streets again on Friday, when the state-sponsored pro-Palestinian Quds Day rallies are held.
