Provided are an apparatus for separating and collecting carbon dioxide and a method of separating carbon dioxide, and more particularly, an apparatus and method of selectively separating carbon dioxide from a byproduct gas using a difference in negative pressure and a difference in carbon dioxide concentration between the inside of a separator, which is made of a ceramic-coated porous silicone membrane and in which the byproduct gas flows, and the outside of the separator in which carbon dioxide is collected.