A total of 404 MPs voted in favor of changing the constitution, while 92 were against, with a two-thirds majority of 367 required.
The initiative, which will have to pass a second round of voting on February 9 before it is approved, was sponsored by the ruling Justice and Development Party. The party has been accused by its opponents of possessing a hidden Islamic agenda due to the suspected connections of many of its MPs with outlawed Islamist groups.
Prime Minister Tayyip Erdogan, who leads the party, had earlier pledged to uphold secular principles enshrined in the constitution.
The Turkish opposition however sees the initiative as a dangerous move which could undermine Turkey's status as a secular state and encourage radical Islamist groups.
The headscarf issue is a source of tension in predominantly Muslim Turkey. Almost two-thirds of Turkish women currently wear a headscarf and many of them stopped attending universities after the traditional Islamic covering was banned on campuses in 1989.
