Abildgaard is a Danish surname. Notable people with the surname include:
Martin Abildgaard (born 2002), Danish gymnast Mette Abildgaard (born 1988), Danish politician Nicolai Abildgaard (1743–1809), Danish painter Oliver Abildgaard (born 1996), Danish footballer (1916–1990), Danish poet (1740–1801), Danish physician and veterinarian Søren Abildgaard (1718–1791), Danish naturalist, writer and illustrator (1826–1884), one of the tenants of the thranite movement