Must it be a jilbāb specifically?

The verse names a specific garment: min jalābībi-hinna. A reasonable question follows: if the face is to be covered by drawing the jilbāb over it, is a woman required to own and wear that particular garment?

The answer

No. What is required is the function: covering, of the described kind. The jilbāb is named because it was the garment in use, not because the obligation attaches to that cut of cloth.

Some scholars, citing the verse together with the ḥadīth of Ummu ʿAṭiyyah in Muslim, held that a woman must wear jilbāb together with khimār when going out or meeting unrelated men.

The counter to this rests on the same ground: what is sought from the jilbāb and khimār is their quality and effect, not their identity as named items.

The comparison is with khimār in prayer: though named specifically in many ḥadīth and reports, no scholar is known to have forbidden replacing it with another cloth that achieves the same purpose. Ibnu al-Mundhir states it directly. It is enough for a woman to pray in one cloth, two, or more, so long as it covers what must be covered in prayer; he did not know of any scholar who required repeating the prayer over the number of cloths used.

ʿIkrimah (d. 105 H), in a report ʿAbd al-Razzāq al-Ṣanʿānī transmits from Yaḥyā b. Abī Kathīr and graded sound, states the khimār half of it plainly: a woman who takes a cloth and covers herself so that no hair shows at all has done what the khimār does. The point about the jilbāb follows the same logic, even though this particular report addresses the khimār.

There is also a practical reason the two garments were worn together in early Islam: the khimār of the time was small, enough only to cover the head and chest, while the larger jilbāb was worn loosely over it to cover what the khimār did not reach. If a jilbāb were worn snugly the way a khimār is, the khimār would no longer be needed — which is why ʿAṭāʾ, asked whether a woman could wear jilbāb without khimār, answered simply: lā yaḍurr — no harm in it. That may also explain why scholars are sometimes found using "khimār" where "jilbāb" would fit better, and vice versa. And it is well known that women since the Prophet's time also used niqab, burqa, and similar garments to cover the face — not the jilbāb alone.

In practice

A long tudung worn with a niqab does what a jilbāb worn over the face does. Nothing turns on the name.

This matters more than it may appear. Framed as a requirement to obtain particular garments, the practice becomes a matter of acquiring the right clothes. Framed as a function, it becomes a question of what is actually covered — which is what the sources are concerned with.

The same principle elsewhere

This is the same shape of question as the ban on niqab during iḥrām: what is regulated is the act, not the tool. In iḥrām, what is forbidden is a specific tool (the niqab) while covering the face by other means remains permitted. Here, what is required is the act of covering; the tool for it is not specified.