The video showed a man in traditional native American dress dancing in the desert.
Dior has since removed all traces of the video, but many savvy social media users had already saved it.
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The tweet - before it was deleted - announced: “An authentic journey deep into the Native American soul in a sacred, founding and secular territory. More to come. September 1st.”
Yahoo UK has contacted Dior for comment.
In the full video, Johnny Depp, who has been the face of the fragrance since 2015, is seen playing a guitar. His co-star Canku One Star of the Rosebud Sioux Tribe performs a warrior dance in a traditional Native American garments alongside him.
Twitter users were particularly disappointed with the fragrance name “Sauvage” being so closely aligned with the word “savage”.
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“Whoever green lighted this is an idiot.” One straight to the point tweet announced.
The hashtag #boycottdior has also started to gain some traction, with disgruntled people using it to express their frustration over the campaign.
Not everybody found the advert offensive though. Many people spoke out in defence of it, describing it as a “homage” to the culture.
Some also reported that Dior collaborated with Americans for Indian Opportunity (AIO) to "ensure respect for indigenous cultures, values and heritage."
Some people argued that every community has “folks willing to consult on stuff like this” but that “it doesn’t protect the company from its decisions”.
This isn’t the first time a brand has been called out for an advert recently.