Šašić is a Bosnian surname. Notable people with the surname include:
Célia Šašić (née Okoyino da Mbabi; born 1988), German football player Milan Šašić (born 1958), Croatian football manager Željko Šašić (born 1969), Serbian pop-folk singer
See also Szvetiszláv Sasics (1948–2025), Hungarian modern pentathlete Šašići, a village in the municipality of Goražde, Bosnia and Herzegovina