We propose a generalized linear low‐rank mixed model (GLLRM) for the analysis of both high‐dimensional and sparse responses and covariates where the responses may be binary, counts, or continuous. This development is motivated by the problem of identifying vaccine‐adverse event associations in post‐market drug safety databases, where an adverse event is any untoward medical occurrence or health problem that occurs during or following vaccination. The GLLRM is a generalization of a generalized linear mixed model in that it integrates a factor analysis model to describe the dependence among responses and a low‐rank matrix to approximate the high‐dimensional regression coefficient matrix. A sampling procedure combining the Gibbs sampler and Metropolis and Gamerman algorithms is employed to obtain posterior estimates of the regression coefficients and other model parameters. Testing of response‐covariate pair associations is based on the posterior distribution of the corresponding regression coefficients. Monte Carlo simulation studies are conducted to examine the finite‐sample performance of the proposed procedures on binary and count outcomes. We further illustrate the GLLRM via a real data example based on the Vaccine Adverse Event Reporting System.