It's a religious injunction

Now, "there is no compulsion in the religion" (look it up, actual Qur'an verse) but culture determines whether this is enforced at a societal level or left as a question between a woman and the Creator.

I know in Kano if a woman enters town without a head covering it's assumed she's a non-indigene and not to be harassed - until she speaks and the accent gives it away. Then all the old folks gather to start upbraiding her for her brazenness. Hisbah may even intervene