Provided are a balloon wrapping apparatus and a balloon wrapping method by which a balloon can be accurately positioned in relation to a pleating section and to a folding section.The balloon wrapping apparatus for wrapping a balloon (52) of a balloon catheter (50) provided with the balloon (52) at a distal portion of an elongated shaft (51) includes: a pleating section (2) that has a plurality of blades (12) aligned with space parts therebetween in a circumferential direction, and that forms the balloon (52) with wing shapes projecting in radial directions by clamping the balloon (52) in the space parts by moving rotationally the blades (12) a folding section (3) that has a plurality of blades (22) aligned in a circumferential direction, and that folds the wing shapes formed in the balloon (52) in the circumferential direction by moving rotationally the blades (22) a support base (4) that supports a part of the shaft (51) which part is on a proximal side of the balloon (52) and a grasping section (110) capable of grasping a part of the balloon catheter (50) which part is on a distal side of the balloon (52).
