NY 251 begins at an intersection with NY 383 in the center of the village of Scottsville, located within the town of Wheatland. It departs Scottsville to the south as River Road and crosses over Oatka Creek before meeting Quaker Road at a rural intersection just south of the village. While River Road continues southward as the unsigned NY 940H, NY 251 turns east to begin its east–west trek across the mostly undeveloped southern portion of Monroe County. After roughly , it crosses over the Genesee River and into the town of Rush, becoming Rush–Scottsville Road in the process. Just inside the town line, NY 251 passes through the hamlet of Industry, a location centered around NY 251's grade crossing with the Livonia, Avon and Lakeville Railroad and the adjacent Rochester & Genesee Valley Railroad Museum.