Yes. Covering the hair, neck and bosom before non-mahram men is an obligation established by the Qur'an, not merely a cultural custom. Allah commands, "and let them draw their head-coverings over their bosoms" (Qur'an 24:31), and, "O Prophet, tell your wives and daughters and the believing women to draw their outer garments over themselves" (Qur'an 33:59). Al-Bukhārī records in his Tafsīr of Sūrat an-Nūr that when the first verse was revealed the women of the Anṣār at once tore pieces from their thick outer wraps and covered themselves, showing that the Companions understood it as a binding command. The scope of the covering (face and hands) is a separate discussion, but the covering of the hair itself is agreed upon.
Evidence — the daleel
On deen2u
Informational, not a personal fatwa. Consult a qualified scholar for rulings on your situation.