Safa Aeli was detained by security forces in Saqqez, western Iran, Ms Amini's brother said on social media on Tuesday afternoon.
His arrest was also reported by human rights organisation Hengaw, which said security forces raided his home before taking Mr Aeli to an unknown location.
About 500 people were killed during months of protests sparked by the death of Ms Amini, who died in the custody of Iran's morality police while visiting Tehran in September.
Her relatives said she was beaten to death after being detained for allegedly wearing her hijab incorrectly.
Demonstrations erupted in her hometown of Saqqez following her funeral, before spreading to every province in the country, with thousands calling for an end to the decades-long rule of Iran's supreme leader Ayatollah Ali Khamenei and authorities that have curtailed women's freedoms.
The relatives of killed protesters are regularly threatened against speaking out and prevented from visiting graves or commemorating their loved ones, and have come under increased pressure as the first anniversary of the protests nears.
Ms Amini's family have previously been the targets of a crackdown.
Her parents and siblings were placed under house arrest as thousands marched to her grave to commemorate 40 days since her passing, uncle Erfan Mortazaei previously confirmed to The National.
Authorities have also desecrated her tombstone and attempted to move her grave, he added.
The parents, siblings and fiancé of Hananeh Kia, a young woman who was shot while on her way home from a dentist appointment, were recently detained.
All have been vocal in criticising the regime over her death.
The pattern of intimidating bereaved relatives is not new.
Loved ones of passengers killed on the Ukrainian Airlines flight shot down over Tehran in 2020 have also spoken of threats and being prevented from burying their own relatives.
Tehran has referred to protesters as "rioters" supported by the West and has executed several people for joining the movement.
Eighteen thousand others were arrested during the protests, which has been used by Tehran to further restrict the rights of women and girls.
Women not wearing the hijab have been barred from their jobs and universities, and have been forced to wash corpses and attend therapy as punishment for defying Iranian law.