The Food and Drug Administration approved for sale a significant advance toward a so-called artificial pancreas for Type 1 diabetes patients, a long-awaited insulin pump that aims to take some of the guesswork out of blood-sugar control.

The product from Medtronic PLC, called the MiniMed 670G, combines two devices that attach to the outside of the body—a pump that delivers insulin through a tiny tube inserted under the skin, and a sensor that monitors blood glucose levels. The monitor tells the pump when to increase or decrease...