Amjad Amini was warned against marking the anniversary of his daughter's death before being released, the Kurdistan Human Rights Network said.
Iran's official IRNA news agency denied that Amjad Amini was arrested, but it did not say if he was briefly detained or warned.
Earlier, social media and reports by rights groups spoke of security forces taking up positions around Amini's home in Saqez, in western Iran.
A massive security force presence was deployed in Iran's mostly Kurdish areas on Saturday in anticipation of unrest, according to human rights groups.
In the protests that followed Amini's death more than 500 people, including 71 minors, were killed, hundreds injured and thousands arrested, rights groups said.
Persons:
Mahsa, Dilara, Mahsa Amini, Amjad Amini, IRNA, Amini's, Saleh Nikbakht, Toby Chopra, Alex Richardson
Organizations:
REUTERS, Kurdistan Human Rights Network, Amnesty International, Thomson
Locations:
Iran, Istanbul, Turkey, Kurdistan, Saqez, Iran's, Iran's Kurdistan