Zelaya or Celaya is a Basque surname. Both are variant spellings of Zelaia, a habitational name in Biscay province, Basque Country, from the Basque language zelai ('field' or 'meadow') and the definite article -a.

Notable people with the surname include: Carlos Zelaya, a graffiti artist who contributed to the video game Skitchin' Emilio José Zelaya (born 1987), Argentine football forward Francisco Zelaya y Ayes (1798–1848), President of Honduras Héctor Ramón Zelaya (Rivera) (born 1958), Honduran football player José Santos Zelaya, president of Nicaragua 1893–1909 Juan Nepomuceno Fernández Lindo y Zelaya (1790–1857), New Spain lawyer and politician, president of Honduras 1847–1852 Luis Selvin Zelaya Bran (born 1979), Salvadoran professional soccer player Manuel Antonio Alberto Zelaya (born 1958), Honduran politician Manuel Zelaya, former president (2006–2009) of Honduras Nelson Fabián Zelaya (born 1973), Paraguayan football defender Raquel Zelaya (born 1945), Guatemalan economist and politician Rodolfo Antonio Zelaya (García) (born 1988), Salvadoran footballer Xiomara Castro de Zelaya, the 56th President and first female President of Honduras