Rivet is a surname. Notable people with the surname include:
André Rivet (1572–1651), French Huguenot theologian Craig Rivet (born 1974), Canadian hockey player Élise Rivet (1890–1945), Catholic nun and war heroine Jeanne Rivet (1850–1913), French composer Louis-Alfred-Adhémar Rivet (1873–1951), Canadian lawyer and politician Paul Rivet (1876–1958), French ethnologist