I've written about this more extensively in the past. But the short version in answer to your specific question would be either the 9th century, the 14th century or the 19th century depending on what exactly you mean.

The earliest discussion of the early Middle Ages as a period where the light of knowledge was growing dark actually comes from the early Middle Ages itself by Walafrid Strabo:

[T]he length and breadth of the kingdom committed to him (i.e. Charlemagne) by God, which was clouded and, if I might say this, nearly completely blind, he made - with light given by God - full of light again, and able to see, by a beaming-out of rays of all learning that was new and in part unknown before to this barbarous age. But now, with the pursuit of knowledge declining again into its opposite, the light of wisdom, because it is less cherished, is growing dimmer in many people. (trans. Janet Nelson, 'The Dark Ages', 192.)

Petrarch is often credited with being the first to refer to the entire Middle Ages up to and including his own era as an era of darkness:

And yet had I touched upon illustrious men of our time, I will not say that I should have introduced your name (lest in my present anger I should seem to flatter you, a thing which is not my habit even when well disposed), but most assuredly I should not have passed over in silence either your uncle or your father. I did not wish for the sake of so few famous names, however, to guide my pen so far and through such darkness. (trans. Theodore E. Mommsen, 'Petrarch's Conception of the "Dark Ages"', 234)

This idea gain currency among the humanists from the 15th century, and the division of history solidified in the 17th century, but the particular terminology of 'The Dark Ages' was actually fairly uncommon before the 19th century and is actually largely restricted to the English language. (For example, in German the analogous phrase would be the 'dark Middle Ages' – das finster Mittelalter.)

It is among these late 19th and early 20th century English historians that the idea of the 'Dark Ages' comes to be used for the early Middle Ages alone, since they begin to adopt it as a contrast to the 'Middle Ages' as a way to distinguish the periods before and after the Norman conquest. (See for example, William Paton Ker's, The Dark Ages (1904).)