Egüez or Eguez is a Spanish surname. Notable people with the surname include:
Iván Egüez (born 1944), Ecuadorian writer Leonardo Eguez (born 1990), Bolivian football manager Eduardo Egüez (born 1959), Argentine lutenist, theorbist, and guitarist Orlando Egüez (1974–2019), Bolivian lawyer and politician Rafael Dávila Egüez (born 1960), Ecuadorian politician and engineer