Morgan City is a city in St. Mary Parish in the State of Louisiana. The population was 12,404 at the 2010 census.Morgan City sits on the banks of the Atchafalaya River. The town was originally named "Tiger Island" by surveyors appointed by U.S. Secretary of War John Calhoun, because of a particular type of wild cat seen in the area. It was later changed for a time to "Brashear City," named after Walter Brashear, a prominent Kentucky physician who had purchased large tracts of land and acquired numerous sugar mills in the area. It was incorporated in 1860.