The relationship between noncoding DNA sequence and gene expression is not well-understood. Massively parallel reporter assays (MPRAs), which quantify the regulatory activity of large libraries of DNA sequences in parallel, are a powerful approach to characterize this relationship. We present MPRA-DragoNN, a convolutional neural network (CNN)-based framework to predict and interpret the regulatory activity of DNA sequences as measured by MPRAs. While our method is generally applicable to a variety of MPRA designs, here we trained our model on the Sharpr-MPRA dataset that measures the activity of ∼500,000 constructs tiling 15,720 regulatory regions in human K562 and HepG2 cell lines. MPRA-DragoNN predictions were moderately correlated (Spearman ρ = 0.28) with measured activity and were within range of replicate concordance of the assay. State-of-the-art model interpretation methods revealed high-resolution predictive regulatory sequence features that overlapped transcription factor (TF) binding motifs. We used the model to investigate the cell type and chromatin state preferences of predictive TF motifs. We explored the ability of our model to predict the allelic effects of regulatory variants in an independent MPRA experiment and fine map putative functional SNPs in loci associated with lipid traits. Our results suggest that interpretable deep learning models trained on MPRA data have the potential to reveal meaningful patterns in regulatory DNA sequences and prioritize regulatory genetic variants, especially as larger, higher-quality datasets are produced.