It was described in Book of Vile Darkness (2002)
Dark Speech is described in greater detail in the D&D 3rd edition product Book of Vile Darkness (2002), p.32-33:
There exists a langauge so dire, so inherently full of spite, malice, corruption, and hatred that it is simply called the Dark Speech. This is the secret language of evil gods, so foul and so potent that even demons and devils refrain from its use, lest it consume them.
In that sourcebook, it can cause one of four known effects: dread (causes those who hear it to be afflicted with fear), power (empowers the caster's spell), corruption (weaken a physical obstacle or object), or dark unity (cause vermin to obey you). Like in 5e, it causes normal humans psychic injury to speak it. The pronunciation of Dark Speech is precise, and without proper training, it can kill the speaker.
Various unique spells and invocations are detailed which include Dark Speech. Some references to it are made in other sourcebooks, such as Complete Arcane, which has a warlock invocation called baleful utterance that is just a syllable of Dark Speech.
A power by the name Dark Speech appears in the D&D 4th edition Book of Vile Darkness (2010), p.20, but it's much less potent.