Protein levels differ considerably between otherwise identical cells, and these differences significantly affect biological function and phenotype. Previous work implicated various noise mechanisms that drive variability in protein copy numbers across an isogenic cell population. For example, transcriptional bursting of mRNAs has been shown to be a major source of noise in the expression of many genes. Additional expression variability, referred to as extrinsic noise, arises from intercellular variations in mRNA transcription and protein translation rates attributed to cell-to-cell differences in cell size, abundance of ribosomes, etc. We propose a method to determine the magnitude of different noise sources in a given gene of interest. The method relies on blocking transcription and measuring changes in protein copy number variability over time. Our results show that this signal has sufficient information to quantify both the extent of extrinsic noise and transcription bursting in gene expression. Moreover, if the mean mRNA count is known, then the relative contributions of transcription versus translation rate fluctuations to extrinsic noise can also be determined. In summary, our study provides an easy-to-implement method for characterizing noisy protein expression that complements existing techniques for studying stochastic dynamics of genetic circuits.