This work is included in some editions of Plutarch's Moralia, a work in Ancient Greek comprising 78 essays.
According to Grove Music, "current scholarship regards it as almost certainly not the work of Plutarch." The Grove article goes on to mention Alexander of Aetolia, Aristoxenus, Glaucus of rhegium and Heraclides Ponticus as people to whom some of the material is currently attributed.
(See also Pseudo-Plutarch, about the hypothetical authors of the essays in some editions of the Moralia - including On Music - that are not believed to have been written by Plutarch.)