There are ancient examples of this kind of thing, to an extent. The Romans didn't sow salt at Carthage, but there is one indication of something comparable: namely, passing a plough over the site of a city to indicate that it is no longer urban but rural.

The idea of erasing a city with a plough is attested as a Roman practice in a few places: Propertius 3.9.41, Horace Odes 1.16.21, Seneca Clem. 1.26.4. These aren't anything to do with Carthage, but they attest to the practice. And there's one late source, an excerpt in the Digest of Justinian, that refers to it being done at Carthage. So we've got thin evidence for it happening at Carthage, but it is a genuine Roman practice.

This doesn't exactly look like ecological warfare, but hear me out. The idea of ploughing is strongly associated with founding a new city, so it makes sense to see the ploughing at a city's eradication as a mirror image of that ritual. That, in conjunction with reports that there was some kind of ritual at Carthage's destruction, perhaps a curse, perhaps an evocatio of Carthaginian Juno, means that it is possible to interpret the Romans using religious means to 'greenify' Carthage. Whether they did so in practical terms as well -- by ploughing it up -- is more doubtful.

The reason this idea of ploughing up Carthage got conflated with the notion of 'salting the earth' (for Mediaeval and early modern interpreters this was a biblical allusion: in Judges 9.45, Abimelech sows the site of Shechem with salt) is because both of them are acts of greenification. Up until the Modern era salt was regularly used as a fertiliser (as it still is in some places for cattle pasture and for asparagus). So turning a bustling city into an uninhabited green space does, I suggest, qualify as a form of ecological warfare -- albeit something you do after you've already won the war, to prevent another war, rather than a strategy for fighting a war.

I wrote an answer here last year that ran through examples of 'salting the earth' as greenification, particularly in the ancient Near East; on Carthage itself, a 1988 note by Susan Stevens, 'A legend of the destruction of Carthage' (Classical philology 83: 39-41) is especially useful. For the 'cursing' of Carthage, see the thread I linked in my second paragraph. The earliest case of someone linking 'ploughing', 'salting the earth', and Carthage under the banner of greenification dates to 1299, when Pope Boniface VIII reported that he destroyed the city of Palestrina and 'subjected it to the plough, following the example of Carthage of old in Africa; and we made salte in it, and commanded that it be sown over'.

Remember, the idea is about sowing salt; and the purpose of sowing isn't to prevent growth! Whether greenification should be regarded as ecological warfare is another question: you'll probably have your own opinion on that.