In view of the frequent uncertain voltage fluctuations and even limit violations at buses caused by the high penetration rate of renewable energy generation and emerging loads, an analytical calculation method for voltage fluctuation intervals under uncertain power disturbances was proposed. This method employed an interval model and a non-parametric approach to characterize uncertainties and could rapidly obtain the voltage fluctuation intervals of each bus through analytical calculations using only the disturbance intervals of bus injected power. On this basis, an optimization model aimed at minimizing the adjustment cost was established to determine the power adjustment measures for mitigating voltage fluctuations, and a voltage fluctuation mitigation strategy utilizing adjustable loads during voltage limit violations was subsequently proposed to restore voltages to the allowable range. Simulation results on the IEEE 39-bus system show that the errors of the upper and lower bounds of the voltage fluctuation intervals obtained by the proposed analytical calculation method are around 1%. Furthermore, the proposed over-limit mitigation strategy is highly effective.