The first collection of madrigals, sung as a set and telling a coherent (and highly comic) story, was Il cicalamento delle donne al bucato (the gossip of women at the laundry), by Alessandro Striggio, which was written in 1567.
Later madrigal comedies are sometimes divided into acts, including a prologue, and while not "acted" in the sense of an opera, they may have been performed on stage with elaborate painted backdrops (for example, the woodcut showing the prologue of Orazio Vecchi's L'Amfiparnaso (1597): a singer is evidently in costume in a backdrop showing a city street).
Vecchi's direction in the score, however, is for the singers not to act, but for the audience to fill in the action internally, using their imagination.
The form was popular especially in the 1590s and few years after 1600, only in Italy, but seems to have fallen out of favor with the advent of opera right at 1600, although a cappella madrigals were also disappearing at this time as well.
Principal composers of madrigal comedy included Alessandro Striggio, Adriano Banchieri, Giovanni Croce, and Orazio Vecchi.