A novel soybean variety, designated XB21Y13 is provided. Also provided are the seeds of soybean variety XB21Y13, cells from soybean variety XB21Y13, plants of soybean XB21Y13, and plant parts of soybean variety XB21Y13. Methods provided include producing a soybean plant by crossing soybean variety XB21Y13 with another soybean plant, methods for introgressing a transgenic trait, a mutant trait, and/or a native trait into soybean variety XB21Y13, methods for producing other soybean varieties or plant parts derived from soybean variety XB21Y13, and methods of characterizing soybean variety XB21Y13. Soybean seed, cells, plants, germplasm, breeding lines, varieties, and plant parts produced by these methods and/or derived from soybean variety XB21Y13 are further provided.