The invention relates to the wheat cultivar designated BZ6W06-451. Provided by the invention are the seeds, plants and derivatives of the wheat cultivar BZ6W06-451. Also provided by the invention are tissue cultures of the wheat cultivar BZ6W06-451 and the plants regenerated therefrom. Still further provided by the invention are methods for producing wheat plants by crossing the wheat cultivar BZ6W06-451 with itself or another wheat cultivar and plants produced by such methods.