Haleh Sahabi, 54, an opposition activist and women's rights campaigner, had been allowed out of jail to attend the funeral of her father Ezatollah Sahabi. She fell in the scuffle and died of a heart attack, the opposition Kaleme website said.
Sources close to the Iranian regime claimed she had died of a pre-existing heart condition.
But the Kaleme website said: "Security forces tried to interfere in the carrying of the body, she objected and security forces confronted her and other people present."
It claimed Ms Sahabi was pushed to the ground. Another opposition site, Sahamnews, said a member of the security forces had punched her in the stomach.
Kaleme said she was holding a picture of her father to her chest and fell when security forces tried to grab it from her. "She fell and did not get up," the website said.