A wheat variety designated W090006C1, the plants and seeds of wheat variety W090006C1, methods for producing a wheat plant produced by crossing the variety W090006C1 with another wheat plant, and hybrid wheat seeds and plants produced by crossing the variety W090006C1 with another wheat line or plant, and the creation of variants by backcrossing, mutagenesis or transformation of variety W090006C1 are disclosed. Methods for producing other wheat varieties or breeding lines derived from wheat variety W090006C1 and to wheat varieties or breeding lines produced by those methods are also provided.