Lead halide perovskite nanocrystals (NCs) have attracted much attention as materials for light-emitting diodes and quantum light sources. A deep understanding of exciton-phonon couplings is essential for obtaining a narrow emission line, weak phonon-sideband photoluminescence (PL), and a long exciton coherence time, which are especially useful for high-color-purity quantum-light-source applications. Here, we report the PL spectra of single CsPbBr3 NCs at 5.5 K as a function of the applied electric field. The exciton peak energy shows an asymmetric parabolic shift for positive and negative biases, implying the presence of a spontaneously generated internal electric field in the NCs when no field is applied. Both the internal electric field and exciton-phonon couplings become larger in smaller NCs, and they have a positive correlation with each other. Our findings show that the exciton-phonon couplings can be manipulated with an electric field, which dominates the PL properties of perovskite NCs.