Brustad is a surname. Notable people with the surname include:
Arne Brustad (1912–1987), Norwegian footballer Bjarne Brustad (1895–1978), Norwegian composer, violinist and violist Eline Gleditsch Brustad (born 1994), Norwegian racing cyclist Fredrik Brustad (born 1989), Norwegian footballer Georg Brustad (1892–1932), Norwegian gymnast Karsten Brustad (born 1959), Norwegian contemporary composer and guitarist Knut Brustad (born 1945), Norwegian middle-distance runner Sylvia Brustad (born 1966), Norwegian politician