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The intrinsic stochasticity of gene expression can lead to a large variability of protein levels across a population of cells. Variability (or noise) in protein distributions can be modulated by cellular mechanisms of gene regulation; in particular, there is considerable interest in understanding the role of post-transcriptional regulation. To address this issue, we propose and analyze a stochastic model for post-transcriptional regulation of gene expression. The analytical solution of the model provides insight into the effects of different mechanisms of post-transcriptional regulation on the noise in protein distributions. The results obtained also demonstrate how different sources of intrinsic noise in gene expression can be discriminated based on observations of regulated protein distributions.