Wedig is a surname. Notable people with the surname include:
Gottfried Wedig (1583–1641), 17th-century German painter Joseph Wedig (1826–???), Member of the Wisconsin State Assembly Kasimir Wedig von Bonin (1691–1752), Prussian lieutenant general Trey Wedig (born 2002), American football player William Wedig (born 1983), American filmmaker