The reaction kinetics underlying the dynamic features of physical systems can be investigated by using various approaches such as the Dynamic Monte Carlo (DMC) method. The usefulness of the DMC method to study reaction kinetics has been limited to systems where the underlying reactions occur with similar frequencies, i.e., similar rate constants. However, many interesting physical phenomena involve sets of reactions with a wide range of rate constants leading to a broad range of relevant time scales. Widely varying reaction rates result in a highly skewed reaction occurrence probability distribution. When the reaction occurrence probability distribution has a wide spectrum, the reactions with faster rates dominate the computations, making the reliable statistical sampling cumbersome. We have developed a probability-weighted DMC method by incorporating the weighted sampling algorithm of equilibrium molecular simulations. This new algorithm samples the slow reactions very efficiently and makes it possible to simulate in a computationally efficient manner the reaction kinetics of physical systems in which the rates of reactions vary by several orders of magnitude. We validate the probability-weighted DMC algorithm by applying it to two model systems: a simple chemical reaction system and a model of vesicular trafficking in living cells.