A novel canola variety designated 45S51 and seed, plants and plant parts thereof, produced by crossing Pioneer Hi-Bred International, Inc. proprietary inbred canola varieties. Methods for producing a canola plant that comprises crossing canola variety 45S51 with another canola plant. Methods for producing a canola plant containing in its genetic material one or more traits introgressed into 45S51 through backcross conversion and/or transformation, and to the canola seed, plant and plant part produced thereby. This invention relates to the canola variety 45S51, the seed, the plant produced from the seed, and variants, mutants, and minor modifications of canola variety 45S51. This invention further relates to methods for producing canola varieties derived from canola variety 45S51.