Unnur is a given name. Notable people with the name include:
Unnur Benediktsdottir Bjarklind (1881–1946), Icelandic poet and prose writer who wrote as Hulda Unnur Birna Vilhjálmsdóttir (born 1984), former winner of the Miss Iceland pageant Unnur Brá Konráðsdóttir (born 1974), Icelandic politician Unnur Steinsson, Miss Iceland 1983
See also Auður (disambiguation), an Icelandic name of which Unnur was originally a variant form Unni - Norwegian equivalent as a given name Hunnur Unni (disambiguation)