It turns out that the song comes not from one of Monteverdi's own books but from a 1624 collection by Carlo Milanuzzi, the Quarto Scherzo delle Ariose Vaghezze. And, deep inside a master's thesis by Cory Gavito of the University of North Texas, there's a facsimile of the original song.
Surprise: above the voice part, there are chords for guitar, just like a modern pop song. The chords are in the Alfabeto system, widespread at the time, in which each common chord is rather arbitrarily assigned a letter of the alphabet. The song opens with chords E, D, H, G which in today's terms are chords of D minor, A minor, B flat major, F major. I'd love to hear what Joni Mitchell would make of it.