In a method for manufacturing an oxygenator, an intermediate spacer is disposed between a cylindrical heat exchange unit configured by winding a first hollow fiber membrane and a cylindrical gas exchange unit configured by winding a second hollow fiber membrane so that a first gap is formed between one end portions of the heat exchange unit and the gas exchange unit, and a first partition section of a first cover member is inserted into the first gap. In such an oxygenator, a first end portion of the intermediate spacer is located at a part that does not overlap the first partition section in a radial direction in the heat exchange unit and the gas exchange unit. The intermediate spacer is formed by winding an intermediate hollow fiber membrane.