The weak itinerant ferromagnetic behavior of Y$_2$Ni$_7$ is investigated through magnetic, transport and calorimetric measurements. The low value of saturation moment, large Rhodes-Wohlfarth ratio, large value of the linear term in heat capacity and Fermi liquid like resistivity behavior with enhanced electron-electron scattering contribution establish firmly the weak itinerant ferromagetic nature of the sample. The critical exponents associated with the paramagnetic to ferromagnetic transition are also investigated from magnetization isotherms using modified Arrott plot, Kouvel-Fisher plot and critical isotherm technique. The more accurate Kouvel-Fisher plot provides the critical exponents to be $\beta$ = 0.306, $\gamma$ = 1.401 and $\delta$ = 5.578. These values are markedly different from the mean field values and correspond closely to the two dimensional Ising spin system with long range spin spin interaction.