Answers provided by Imam Muḥammad Saʿīd Ramaḍān al-Būṭī, may Allah have mercy on him
What is the ruling for a woman using a public car (i.e. a taxi) by herself and does the ruling differ if there are people on the road or not – such as the outskirts of a city for example? Also, is the ruling attached to necessity (ḍarūrah) or not – for example if she only wanted to visit her friend?
It is unlawful for a woman to be alone (khalwah) with a foreign man, and what I’m about to say is personal reasoning (ijtihād) based on that fact. As long as the car is moving within the streets of a city and its windows are transparent then her being with the driver is not considered khalwah, but if the car goes outside of built up areas and into the countryside and the like then that would be khalwah and therefore unlawful.
What is the ruling in the Revealed Law regarding women driving cars?
The ruling that it is permissible for women to drive cars follows from the ruling that it is permissible for women to mount and ride camels, and the Messenger of Allah, may Allah bless him and grant him peace, has established the second ruling by consensus.
[Translated from Mashūrāt Ijtimāʿiyyah (Damascus: Dār al-Fikr, 2003), p.152-153]