“And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts, etc.)…” [Soorah Noor(24):31]
Ibn ‘Uthaymeen comments saying:
“Allaah commands the believing women to guard their private parts. This command is a command for guarding the private parts as well as all of the means that eventually lead to that. And there is no doubt for one who has common sense that from the means that lead towards guarding the private parts is the veiling of the face. This is since exposing it is a cause for drawing looks towards it, reflecting on its features and finding pleaser in that. And consequently this leads to a man trying to communicate and get in touch with a woman.
In a hadeeth the Prophet (saw) said:
“The eyes commit zinaa (fornication) and their zinaa is looking… The heart ardently desires and awaits, and the private parts either confirm it or deny it.” [Bukhaaree & Muslim]
So if covering the face is one of the means that ultimately leads towards guarding ones private parts, then indeed it was commanded since the means take on the same ruling as the objective.”
[Taken from “Four Essays On The Obligation Of Veiling” Ch. 2: An Essay On Hijaab, Pp. 28-29]