A soybean cultivar, designated 0037357, is disclosed. The invention relates to the seeds of soybean cultivar 0037357, to the plants of soybean 0037357 and to methods for producing a soybean plant produced by crossing the cultivar 0037357 with itself or another soybean variety. The invention further relates to hybrid soybean seeds and plants produced by crossing the cultivar 0037357 with another soybean cultivar.