To provide a cloth clamping chuck and a cloth handling apparatus that can handle cloth so as to reduce falling of the cloth while avoiding damage to the cloth. A cloth clamping chuck 21 includes a pair of clamps 212, 213 disposed facing each other, and an opening-closing means that moves the pair of clamps 212, 213 relatively closer to or separated from each other. Each of the clamps 212, 213 has, at a leading end, a projecting part 214 or 215 that projects toward the other opposite clamp 213 or 212. Each of surfaces 214a, 215a of the projecting parts 214, 215 on a base end side of the clamps 212, 213 is formed either as a flat surface parallel to a facing direction of the pair of clamps 212, 213 or as an inclined surface inclining toward the above base end side while extending toward the other opposite projecting part 215 or 214.