Munday is a city in Knox County, Texas, United States. The population was 1,527 at the 2000 census. The 2010 U.S. Census Bureau placed the population at 1,300.The Texas politician Orville Bullington practiced law in Munday early in the 20th century and was the Knox county attorney before he ran as the Republican gubernatorial nominee in 1932 against Miriam Ferguson.