Madras is a city in Jefferson County, Oregon, United States. Originally called "The Basin" after the circular valley the city is in, it is unclear whether Madras was named in 1903 for the cotton fabric called "Madras" that originated in the city of Madras in Tamil Nadu, India, or from the name of the city itself. The population was 6,046 at the 2010 census. It is the county seat of Jefferson County.