It's helpful to think of the Renaissance less as an era, and more as a cultural movement emphasizing Greco Roman ideals, which began in the 14th century and lasted into the 16th. Periodization is tricky, but the Sack of Rome in 1527 is often used as the end point of the Renaissance in Italy. The capstone for the Middle Ages is usually thought of as the late 15th Century, with the discovery of the Americas, the fall of the Byzantine Empire, the rise of gunpowder armies and centralized states, and the proliferation of the printing press and the Protestant Reformation it facilitated. This subsequent period is called the Early Modern Period, and it lasted until the French Revolution.

As you can see, there's quite a long period of overlap between the Renaissance and the Middle Ages; in that sense, you can think of it as sudden cultural change within polities whose social and political landscapes were adjusting to different forces than those that spurred the Renaissance.