The ϕ-Λ(1520) interference effect in the γp→K^{+}K^{-}p reaction has been measured for the first time in the energy range from 1.673 to 2.173 GeV. The relative phases between ϕ and Λ(1520) production amplitudes were obtained in the kinematic region where the two resonances overlap. The measurement results support strong constructive interference when K^{+}K^{-} pairs are observed at forward angles but destructive interference for proton emission at forward angles. Furthermore, the observed interference effect does not account for the sqrt[s]=2.1 GeV bump structure in forward differential cross sections for ϕ photoproduction. This fact suggests possible exotic structures such as a hidden-strangeness pentaquark state, a new Pomeron exchange, or rescattering processes via other hyperon states.