Biochemical reactions that involve small numbers of molecules are accompanied by a degree of inherent randomness that results in noisy reaction outcomes. In synthetic biology, the ability to minimize noise particularly during the reconstitution of future synthetic protocells is an outstanding challenge to secure robust and reproducible behavior. Here we show that by encapsulation of a bacterial cell-free gene expression system in water-in-oil droplets, in vitro-synthesized MazF reduces cell-free gene expression noise >2-fold. With stochastic simulations we identify that this noise minimization acts through both increased degradation and the autoregulatory feedback of MazF. Specifically, we find that the expression of MazF enhances the degradation rate of mRNA up to 18-fold in a sequence-dependent manner. This sequence specificity of MazF would allow targeted noise control, making it ideal to integrate into synthetic gene networks. Therefore, including MazF production in synthetic biology can significantly minimize gene expression noise, impacting future design principles of more complex cell-free gene circuits.