Sunday night's assault took place as thousands of people enjoyed inauguration festivities, raising new worries about Egypt's commitment to fighting sexual violence.
Authorities arrested seven men aged between 15 and 49 for sexually harassing women on Tahrir Square after the posting of the video, which caused an uproar in local and international media.
Get breaking news and insider analysis on the rapidly changing world of media and technology right to your inbox.
It was not clear whether the men arrested took part in the assault shown on the video.
"The Egyptian embassy in Washington, D.C. and a number of Egyptian authorities, at the direction of President Abdel Fattah el-Sissi, have requested the YouTube administration to remove the video of the sexual assault victim," the president's spokesman said.
"This came in response to her wish, which she expressed during the president's visit to her yesterday at the hospital to check on her condition," he added in an emailed statement late on Thursday.
Sexual harassment, high rates of female genital mutilation and a surge in violence after the Arab Spring uprisings have made Egypt the worst country in the Arab world to be a woman, a Thomson Reuters Foundation survey showed late last year.