Fletcher was platted in 1830. The village was named after Samuel Fletcher, a local storekeeper. The post office that had been in operation at Fletcher since 1831 closed in 2010. According to the United States Census Bureau, the village has a total area of 0.31 square miles (0.80 km²), all land. Fletcher is drained by East Branch Lost Creek and West Branch Lost Creek. The village is crossed by U.S. Route 36 and State Route 589.