Bjørnstad is a Norwegian surname. Notable people with the surname include:
Hans Bjørnstad (1928–2007), Norwegian ski jumperHenrik Bjørnstad (born 1979), Norwegian professional golferJørgen Bjørnstad (1894–1942), Norwegian gymnastKetil Bjørnstad (born 1952), Norwegian pianist and composerOlaf B. Bjørnstad (1931–2013), Norwegian former ski jumperOlav Bjørnstad (1882–1963), Norwegian rowerTor Halvor Bjørnstad (born 1978), Norwegian cross-country skierVidar Bjørnstad (born 1955), Norwegian politician for the Labour Party