Shatsk is a town and the administrative center of Shatsky District in Ryazan Oblast, Russia, located on the Shacha River 145 kilometers …Shatsk is a town and the administrative center of Shatsky District in Ryazan Oblast, Russia, located on the Shacha River 145 kilometers southeast of Ryazan, the administrative center of the oblast. Population: 6,561 ; 7,563 ; 8,181.