In this paper, a stochastic Kawasaki disease model was investigated. First, it was theoretically proved that the solution of the stochastic model is positive and global, as well as the existence of an ergodic stationary distribution. Subsequently, we derived the exact expression of the probability density function around a quasi-equilibrium point through the four-dimensional Fokker-Planck equation. Finally, some numerical simulations were introduced to validate the theoretical findings.