Jamesburg, New Jersey. Jamesburg is a borough in Middlesex County, New Jersey, United States. As of the 2010 United States Census, the borough's population was 5,915, reflecting a decline of 110 (-1.8%) from the 6,025 counted in the 2000 Census, which had in turn increased by 731 (+13.8%) from the 5,294 counted in the 1990 Census. 1 History.