The strong spin-orbital coupling and intense optical transition in lead halide perovskites enable facile optical injection and manipulation of spin states potentially useful for spintronics, one manifestation of which is the optical Stark effect (OSE). A strong OSE would benefit from discrete energy levels and a strong band edge transition with concentrated oscillator strength, which can be realized in three-dimensionally confined quantum dots (QDs). This idea, however, has not been explored yet for perovskite materials. Here we report the observation of strong OSE in perovskite colloidal QDs using circularly polarized transient absorption spectroscopy. The large OSE shifts correspond to transition dipoles as large as 52 D, which compares favorably to those recently reported for higher-dimensional perovskites as well as transition metal dichalcogenide monolayers. Colloidal synthesis also allows for facile tuning of the OSE spectral ranges of perovskite QDs via sizes and compositions, and the impact of these parameters on the OSE is examined, providing fundamental insights into the band edge transition of lead halide perovskites.