The minister told the Egyptian daily, al-Masri Al-Youm: "There was an age when our mothers went to university and worked without the veil. It is in that spirit that we grew up. So why this regression?"
Hosni offered his resignation after the the Muslim Brotherhood, Egypt's largest Islamic political group, called for the minister to "apologise and resign", calling his remarks insults that were directed at Islam's religious leaders.
Saudi Arabia's leading Muslim scholar described the Egyptian culture minister's recent criticism of the veil as a "calamity," a Saudi satellite channel reported.
Sheikh Abdul-Aziz Al al-Sheikh, Saudi Arabia's Grand Mufti, responded in a statement aired by Al Majd television, a religious channel, to Hosni's comments.
"It is a calamity that struck Islamic lands and contradicts the teachings of the Quran," al-Sheikh said of Hosni's comments. "It is truly painful to hear such declarations from within Islamic lands, from people who are considered Muslims."
The response to the Egyptian minister's remarks highlights the growing conflict between conservative Muslims and secularists in the Arab world. It is also an example of the struggle between secular governments, such as Egypt, and Islamic opposition groups.
Headscarves fell out of favour among some urban Egyptian women in the 1920s and 1930s, but began reappearing in the 1970s and 1980s. The evolution has been steady with more women wearing scarves, and more also wearing body cloaks and face veils.
Salah Zeidan, a scholar at Al-Azhar University, the Sunni Arab world's most important seat of learning, said Hosni's statements puts him "in a critical position" and "will take him down".
"This is degrading talk that does not fit a sophisticated man, especially a minister," Zeidan said.
"He should know that with these remarks he has just isolated himself from his Islamic community. He has to watch out if he walks out in the street, because any veiled woman will pour her raging fire on him," he said.