Bundgaard is a surname. Notable people with the surname include:
Anders Bundgaard (1864–1937), Danish sculptor Filip Bundgaard (born 2004), Danish footballer Henrik Bundgaard (born 1975), Danish footballer Oliver Bundgaard (born 2001), Danish footballer Poul Bundgaard (1922–1998), Danish actor and singer Scott Bundgaard (born 1968), American politician Sine Bundgaard (born 1970), Danish soprano Søren Bundgaard, a member of the music group Hot Eyes