The petition is titled "End injustice: We want a solution, not postponement."
The creators of the petition don't wear headscarves themselves, but said they object to discrimination against women who do.
"We oppose every kind of practice that creates inequality for women who wear headscarves," the petition states.
The petition calls on politicians to change legislation that prevents women wearing headscarves from enjoying their rights.
The petition received more than 2,000 signatures almost immediately after being posted online, Today's Zaman said.
Turkey banned headscarves for civil servants in the 1980s, and the regulation was tightened in 1997.
Now, state offices don't hire women who wear a headscarf, Today's Zaman said, and the women who do wear a headscarf are often denied employment at most private companies, even there is no ban for such businesses.
Women wearing headscarves are also not elected to Parliament, Today's Zaman said.