The company added that it wouldn't include the outfit in the show's TV broadcast next month, or in any marketing materials.
Headdresses are a symbol of respect, worn by Native American war chiefs and warriors. For Great Plains tribes, for instance, each feather placed on a headdress had to be earned through an act of compassion or bravery.
"When you see a Lakota chief wearing a full headdress, you know that he was a very honourable man.
"He was a leader. He did a lot of honourable things for his people," said Michelle Spotted Elk, a Santa Cruz, California, woman of mixed heritage whose husband is Lakota.
Victoria's Secret model Karlie Kloss (right) walked on to the runway wearing the floor-length feathered headdress, leopard-print underwear and high heels.