An interval observer is designed for multi-rate systems with multiplicative noises in this paper. First, a multi-rate sampling system is investigated. At the same time, the presence of multiplicative noise would couple with the multi-rate sampling mechanism, which brings a significant challenge for the estimate of the system states. To address this problem, some arithmetic rules are proposed to separate the noise-contaminated terms, and the multi-rate system is transformed into an equivalent system with a uniform sampling period using the lifting technique and augmentation methods. Based on this, an interval observer is developed to estimate the bounds of the system states, sufficient conditions to ensure the effectiveness of the interval observer, and the input-to-state stability (ISS) of the estimation error dynamics are derived. Finally, simulations verify the proposed method.