A novel soybean cultivar, designated 0491737, is disclosed. The invention relates to the seeds of soybean cultivar 0491737, to the plants of soybean 0491737 and to methods for producing a soybean plant produced by crossing the cultivar 0491737 with itself or another soybean variety. The invention further relates to transgenic soybean plants produced by transforming a soybean of the cultivar 0491737.