Schulenburg is a city in Fayette County, Texas, United States. Its population was 2,633 at the 2020 census. Known for its German cult…Schulenburg is a city in Fayette County, Texas, United States. Its population was 2,633 at the 2020 census. Known for its German culture, Schulenburg is home of the Texas Polka Music Museum. It is in a rural, agricultural area settled by German and Czech emigrants in the 1800s.