Wordorigins.org

A hag is an ugly, and often evil, woman. The etymology is usually conjectured to be a clipping of the Old English hægtesse, a witch or fury.

It first appears in the 13th century in the form hegge. From the monastic text Ancren Riwle, written sometime before 1225:

Þe seoue moder sunnen..and of hwuche mesteres þeo ilke men serueð...þet habbeð iwiued o þeos seouen heggen.
(The seven mother sons...and of which masters that same men serve...that have married of these seven hags.)

It appears again the 14th century in William Langland’s Piers Plowman from 1377 (B Text):

With two blered eyghen as a blynde hagge.
(With two gouged eyes as a blind hag.)

These are the only known uses of the term prior to the 16th century, when it enters into common use. The first sense in the later use is that of an evil spirit. From Thomas Elyot’s 1538 Dictionary:

Larua, a spyrite whiche apperethe in the nyght tyme. Some do call it a hegge, some a goblyn.

Shakespeare picks up where Langland left off and uses the term in the sense of an ugly woman in his 1611 The Winter’s Tale:

A grosse Hagge: And Lozell, thou art worthy to be hang’d, That wilt not stay her Tongue.

There is a modern conjecture, popular among New Age feminists that hag comes from the Greek hagia, or holy. This is clearly an attempt to deliberate reclaim and meliorate the term’s meaning. There is no known connection between the Old and Middle English uses and the Greek. The two terms do not even share the same Indo-European root. So this popular etymology is just false.

(Source: Oxford English Dictionary, 2nd Edition)