Fibiger is a surname. Notable people with the surname include:
Arnold Fibiger (1847–1915), Polish piano builder Elfride Fibiger (1832–1911), Danish writer Ilia Fibiger (1817–1867), Danish writer Jesse Fibiger (born 1978), Canadian hockey player Johannes Fibiger (1867–1928), Danish pathologist Mathilde Fibiger (1830–1872), Danish writer
Other Fibiger (crater), lunar crater