Vatican City is the smallest sovereign state in the world by area that uses the euro as its official currency. The city-state covers only about 0.49 square kilometres and issues euro coins under an agreement with the European Union through Italy.
Vatican City is not an EU member, but it has a monetary agreement that permits euro use and allows it to mint limited Vatican euro coins. These coins are legal tender throughout the euro area, although collectors often seek them because of their small mintages and distinctive designs.
Monaco, San Marino and Andorra also use the euro without being EU member states, but all are larger than Vatican City. The question concerns official currency use, not membership in the euro area or European Union.