An interesting question. It takes place in the Renaissance, but not in any specific period beyond that. (There aren't, for example, clear references to specific kings or historical events that would tie it down.) It also isn't possible to really pin it down through the setting. Shakespeare sets the play in Messina, in Sicily, but there aren't any real references there to anything that would anchor it more fully. It has been suggested that the society portrayed in the play is artificial—that it doesn't really represent Messina or a specific period, but is a kind of Italian mishmash.
'Much Ado About Nothing' is set in 16th Century Italy in a city named Messina.