Matthews was named for C. D. Matthews, a settler who lived in the area from the 1870s onward. A community developed on the site following the building of a branch line of the St. Louis and San Francisco Railroad near the turn of the century, and it was used as a shipping station for the Scott County Milling Company of Sikeston for several years. A post office was established by 1904.
Matthews is located near the intersection of U.S. Route 62 and Missouri State Highway 80 in northern New Madrid County, about eight miles south of Sikeston and twelve miles north of New Madrid. Its exact coordinates are 36°45’28”N 89°35’12”W. Interstate 55 runs about one mile to the east.
The city mostly lies on Sikeston Ridge, a low north-south sand ridge that stretches from Sikeston to New Madrid. It has a total land area of 1.96 square miles, and an average elevation of 312 feet.
At the 2010 census, Matthews had a total of 628 inhabitants, grouped into 247 households, with a population density of 320.4 people per square mile. This figure represented a slight increase from the 2000 census, when Matthews had a population of 605. 97.13% of the inhabitants were White, 1.91% were African-American, 0.48% were Native American, 0.16% were from some other race, and 0.32% were from two or more races. Hispanics of any race were 0.32% of the population.
The median age in Matthews was 48.8 years, with 16.7% of inhabitants under the age of 18, 6.1% between 18 and 24 years old, 23.3% between 25 and 44, 32.7% between 45 and 64, and 21.0% 65 years old or older. The sex ratio was 46.0% male, 54.0% female.
According to the 2010 American Community Survey, the median household income in Matthews was $34,625, and the median family income was $38,462. The unemployment rate was 1.4%. The per capita income was $16,233. About 15.2% of the population lived below the poverty line, including 15.1% of people under the age of 18 and 10.2% of people 65 years old or older.