The invention relates to the novel cotton variety designated MX0623B2RF. Provided by the invention are the seeds, plants, plant parts and derivatives of the cotton variety MX0623B2RF. Also provided by the invention are tissue cultures of the cotton variety MX0623B2RF and the plants regenerated therefrom. Still further provided by the invention are methods for producing cotton plants by crossing the cotton variety MX0623B2RF with itself or another cotton variety and plants produced by such methods.