The cotton variety FM 1621GL is disclosed. The invention relates to seeds, plants, plant cells, plant tissue, harvested products and cotton lint as well as to hybrid cotton plants and seeds obtained by repeatedly crossing plants of variety FM 1621GL with other plants. The invention also relates to plants and varieties produced by the method of essential derivation from plants of FM 1621GL and to plants of FM 1621GL reproduced by vegetative methods, including but not limited to tissue culture of regenerable cells or tissue from FM 1621GL.