The father of the victim said that they had gathered for a peaceful demonstration against the release of the juvenile convict but the police detained them.
"Is there no justice in this country?" he asked.
However, police said that the parents were "not detained" but just removed from the road "for their safety".
"We detained around 40 youths who had blocked a stretch on the Outer Ring Road but the parents of the victim were not detained. They were removed from the road for their safety, put on a van and brought to the operation cell in Maurice Nagar and later we arranged for their transportation to be taken back home," said DCP (North) Madhur Verma.
Delhi Chief Minister Arvind Kejriwal termed the detention as "unacceptable" and said he has asked Chief Secretary KK Sharma to talk to Police Commissioner BS Bassi to secure the release of the victim's parents.
"I am shocked to learn that Nirbhaya's parents have been detained. They should immediately be released. Police action against Nirbhaya's parents is unacceptable. I have asked Chief Secy to talk to Police Commissioner and get them released," he tweeted.
However, the father of the victim accused the Delhi government of trying to shield the convict, who has now turned 20.
The protesters staged the demonstration at the Outer Ring Road stretch near the correction home, where the juvenile convict was put up, and allegedly blocked the road causing traffic congestion in the area.
Members of Delhi University Students Union and Jawaharlal Nehru University Students Union had earlier staged a protest at Jantar Mantar demanding the convict juvenile should not be released.
Later, the students along with the victim's parents held a protest outside the juvenile home and shouted slogans that the government should take immediate steps to stop his release.
Nirbhaya's mother Asha Devi on Saturday said, "The prime minister travels the world, but there is no law for women here. Everyone promises change but nothing has been done."
"We have been waiting for justice for three years. The government and judiciary have given up on us. Rapists have been given a report card that you can rape and you will give you machine and money and will protect you by forming a committee," he said.