In clonally propagated crops, non-additive genetic effects can be effectively exploited by the identification of superior genetic individuals as varieties. Cassava (Manihot esculenta Crantz) is a clonally propagated staple food crop that feeds hundreds of millions. We quantified the amount and nature of non-additive genetic variation for key traits in a breeding population of cassava from sub-Saharan Africa using additive and non-additive genome-wide marker-based relationship matrices. We then assessed the accuracy of genomic prediction of additive compared to total (additive plus non-additive) genetic value. We confirmed previous findings based on diallel populations, that non-additive genetic variation is significant, especially for yield traits. Further, we show that we total genetic value correlated more strongly to observed phenotypes than did additive value, although this is constrained by low broad-sense heritability and is not beneficial for traits with already high heritability. We address the implication of these results for cassava breeding and put our work in the context of previous results in cassava, and other plant and animal species.