The footage shows a crowd of men surrounding the young woman, who was stripped off her clothes and badly bruised, as police escorted her to an ambulance following Sunday's attack on Cairo's iconic Tahrir Square.
Shared widely on social media websites like YouTube, Facebook and Twitter, it appears to have been filmed using a mobile telephone.
A security official authenticated the video, saying police had arrested seven men for assaulting and stripping the 19-year-old student.
The woman was transferred to a hospital and prosecutors had been asked to investigate the attack, the official said, alleging the seven were also involved in three other cases of sexual harassment.
"Sexual harassment in Tahrir... is absolutely disgusting. I have no words. So appalled and ashamed," said one Twitter user.
The Egyptian interior ministry said police had arrested seven men aged 16 to 49 as "they had (sexually) harassed a number of girls during the celebrations in the Tahrir area".
It did not specify whether the seven were involved in the assault of the girl seen in the video.
"It is shameful that security officials from the interior ministry did not adopt any measures or security plans to prevent such assaults, despite the fact they have repeatedly occurred," said the "I Saw Harassment" activist group.
It said it had documented five cases of sexual assault by mobs, with four victims needing medical aid on Sunday.
Egypt has been plagued by rampant sexual harassment cases, with more than 99 percent of women subjected to some form of such abuse, the United Nations said in a study issued last year.
Women in the North African country said that they are harassed regardless of whether they wear conservative Islamic attire or Western-style clothes.
But since the revolution that toppled long-time president Hosni Mubarak in 2011, the problem has worsened, with women now being regularly attacked during rallies by groups of men in and around Tahrir Square.
Almost 100 women were sexually assaulted during the four days of mass protests that led to the military ouster of Islamist president Mohamed Morsi in July last year, Human Rights Watch reported at the time.
Sunday's attacks come days after the presidency approved new punishments for sexual harassment, entailing hefty fines and jail terms for offenders.
Sisi, the former army chief who deposed Morsi, was sworn in on Sunday amid mass celebrations organised by the authorities, after winning last month's presidential election in a landslide.