We report an in-plane optical spectroscopy study on the newly discovered iron-selenide superconductor K$_{0.75}$Fe$_{1.75}$Se$_2$. The measurement revealed the development of a sharp reflectance edge at very low frequency below T$_c$ on the relatively incoherent electronic background. The phenomenon was explained as arising from the Josephson-coupling plasmon of superconducting condensate. Together with the transmission electron microscopy analysis, our study yields compelling evidence for the presence of nanoscale stripe-type phase separation between superconductivity and magnetism.