The original post, which has now been deleted, came with a disclaimer warning the image was "not about race change".
However another post, using both the image of the model and the original disclaimer, has been uploaded.
The new caption says: "I can't offer an apology for my artwork, and for what I find to be beautiful."
The make-up artist, whose given name is not revealed on his Instagram account, offered an explanation for his decision to use a white model.