Genome-wide association studies (GWASs) examine the association between genotype and phenotype while adjusting for a set of covariates. Although the covariates may have non-linear or interactive effects, due to the challenge of specifying the model, GWAS often neglect such terms. Here we introduce DeepNull, a method that identifies and adjusts for non-linear and interactive covariate effects using a deep neural network. In analyses of simulated and real data, we demonstrate that DeepNull maintains tight control of the type I error while increasing statistical power by up to 20% in the presence of non-linear and interactive effects. Moreover, in the absence of such effects, DeepNull incurs no loss of power. When applied to 10 phenotypes from the UK Biobank (n = 370K), DeepNull discovered more hits (+6%) and loci (+7%), on average, than conventional association analyses, many of which are biologically plausible or have previously been reported. Finally, DeepNull improves upon linear modeling for phenotypic prediction (+23% on average).