As missing values are frequently present in genomic data, practical methods to handle missing data are necessary for downstream analyses that require complete datasets. State-of-the-art imputation techniques including Singular Value Decomposition (SVD) and K-Nearest Neighbors (KNN) based methods can be computationally expensive for large datasets and it is difficult to modify these algorithms to handle certain missing-not-at-random cases. In this work, we use a deep learning framework based on the variational autoencoder (VAE) for genomic missing value imputation and demonstrate its effectiveness in transcriptome and methylome data analysis. We show that in the vast majority of our testing scenarios, VAE achieves similar or better performances than the most widely used imputation standards, while having a computational advantage at evaluation time. When dealing with missing-not-at-random, e.g. low values are missing, we develop simple yet effective methodologies to leverage the prior knowledge about missing data. Furthermore, we investigate the effect of varying latent space regularization strength in VAE on the imputation performances, and in this context show why VAE has a better imputation capacity compared to a regular deterministic autoencoder (AE).