Arostegui or Aróstegui is a surname. Notable people with the surname include:
Alfonso Clemente de Aróstegui (1698–1774), Spanish bishop, writer, lawyer and diplomat Consuelo Luz Arostegui, American singer Gonzalo de Quesada y Aróstegui (1868–1915), Cuban diplomat Juan Arostegui (born 1980), Argentine soccer player Manuel de Aróstegui Sáenz de Olamendi (1758–1813), Spanish politician María de las Mercedes Adam de Aróstegui (1873–1957), Cuban pianist and composer Xabier López-Arostegui (born 1997), Spanish basketball player