Within individual cells, two molecular processes have been implicated as sources of noise in gene expression: (i) Poisson fluctuations in mRNA abundance arising from random birth and death of individual mRNA transcripts or (ii) promoter fluctuations arising from stochastic promoter transitions between different transcriptional states. Steady-state measurements of variance in protein levels are insufficient to discriminate between these two mechanisms, and mRNA single-molecule fluorescence in situ hybridization (smFISH) is challenging when cellular mRNA concentrations are high. Here, we present a perturbation method that discriminates mRNA birth/death fluctuations from promoter fluctuations by measuring transient changes in protein variance and that can operate in the regime of high molecular numbers. Conceptually, the method exploits the fact that transcriptional blockage results in more rapid increases in protein variability when mRNA birth/death fluctuations dominate over promoter fluctuations. We experimentally demonstrate the utility of this perturbation approach in the HIV-1 model system. Our results support promoter fluctuations as the primary noise source in HIV-1 expression. This study illustrates a relatively simple method that complements mRNA smFISH hybridization and can be used with existing GFP-tagged libraries to include or exclude alternate sources of noise in gene expression.