Priyanka and Rahul Gandhi, brother and sister and leaders of the main opposition Congress Party, were held as they made their way to the victim's home in Hathras, about 62 miles from the capital New Delhi.
The siblings are descended from three former Indian prime ministers.
In a video published by the ANI news agency, Rahul was seen jostling with police before falling to the ground.
Dozens of Congress Party workers scuffled with the officers, who used sticks to disperse them.
It came after the unnamed victim died on Tuesday from injuries sustained when she was attacked in a field near her home in northern Uttar Pradesh state on 14 September.
The 19-year-old woman was from the Dalit community, whose members often face violence and discrimination.
Four men - who are from a higher caste, or class, according to the victim's brother - have been arrested.
Twenty-five people were arrested after protesters clashed with police in various parts of the country on Wednesday after officers cremated the woman's body.
Her brother said that was against the wishes of her family, who had wanted to bury her, but local officials deny this.
Gatherings of five or more people have been banned due to the coronavirus pandemic and authorities have said other politicians would be prevented from visiting the area.
The victim and her brother are not being identified due to laws against naming victims of sexual violence.
India is one of the world's most dangerous places for women, with a rape occurring every 15 minutes, according to federal data - figures that rights groups say vastly underestimate the scale of the problem.
Uttar Pradesh - with a population of more than 200 million people, and ruled by Prime Minister Narendra Modi's Bharatiya Janata Party - ranks as particularly unsafe for women.
Opposition leaders have highlighted several other violent incidents in Uttar Pradesh in recent days, including allegations of a similar gang-rape of a Dalit woman in Balrampur.
The Congress Party said other senior members were also detained, but did not provide details.