The two-particle momentum correlation function of a K^{-}p pair from high-energy nuclear collisions is evaluated in the K[over ¯]N-πΣ-πΛ coupled-channel framework. The effects of all coupled channels together with the Coulomb potential and the threshold energy difference between K^{-}p and K[over ¯]^{0}n are treated completely for the first time. Realistic potentials based on the chiral SU(3) dynamics are used which fit the available scattering data. The recently measured correlation function is found to be well reproduced by allowing variations of the source size and the relative weight of the source function of πΣ with respect to that of K[over ¯]N. The predicted K^{-}p correlation function from larger systems indicates that the investigation of its source size dependence is useful in providing further constraints in the study of the K[over ¯]N interaction.