A novel soybean variety, designated XB32AE13 is provided. Also provided are the seeds of soybean variety XB32AE13, cells from soybean variety XB32AE13, plants of soybean XB32AE13, and plant parts of soybean variety XB32AE13. Methods provided include producing a soybean plant by crossing soybean variety XB32AE13 with another soybean plant, methods for introgressing a transgenic trait, a mutant trait, and/or a native trait into soybean variety XB32AE13, methods for producing other soybean varieties or plant parts derived from soybean variety XB32AE13, and methods of characterizing soybean variety XB32AE13. Soybean seed, cells, plants, germplasm, breeding lines, varieties, and plant parts produced by these methods and/or derived from soybean variety XB32AE13 are further provided.