Damgaard is a Danish surname. Notable people with the surname include:
Emil Damgaard (born 1998), Danish footballer Holger Damgaard (1870–1945), Danish photographer Jesper Damgaard (born 1975), Danish ice hockey player Laura Damgaard (born 1996), Danish handball player Malinda Damgaard (born 1981), Swedish milliner Michael Damgaard (born 1990), Danish handball player Thais Damgaard (born 2000), Danish footballer Thomas Damgaard (born 1971), Danish boxer Thorbjørn Damgaard, Norwegian footballer
See also Hans Fuglsang-Damgaard (1890–1979), Danish Lutheran bishop Damsgaard