Fürstenhagen is a district of the municipality of Lutter and part of the administrative community of Uder. It is the youngest village in the district of Eichsfeld in Thuringia and one of the smallest with 60 inhabitants. Fürstenhagen is a Roman Catholic village and is located about 6 kilometers southwest of Heilbad Heiligenstadt on the Obereichsfelder Höhe at 496 m above sea level (highest point at the former train station).