The critical behavior of infinite-layer La$_{0.825}$Sr$_{0.175}$MnO$_3$ of Ruddlesden-Popper series manganite has been studied around the transition temperature ($T_C$). To reveal the universality class that explains the critical behavior in La$_{0.825}$Sr$_{0.175}$MnO$_3$ several methods, such as modified Arrott plots, Kouvel-Fisher, entropy and critical isotherm analysis have been employed. The critical exponent $\delta$ for infinite-layer is obtained independently from critical magnetization isotherm and found to satisfy the Widom scaling relation $\delta = 1+\gamma/\beta$. The universality class of the critical phenomenon in infinite-layer La$_{0.825}$Sr$_{0.175}$MnO$_3$ manganite can be explained with the help of renormalization group theory approach for three dimensional (3D) systems. We have shown that a short-range 3D-Ising type interaction is responsible for ferromagnetic and second-order phase transition to paramagnetic phase.