In this study we used the observed perihelion precession of planetary orbits in the Solar System in order to constrain theory of Yukawa-type gravity, and to bound mass of graviton. For that purpose we assumed that the precession angles of the planets in Yukawa-type gravity should be equal to their observed values, as well as to the corresponding predictions of General Relativity (GR). Starting from these requests we constrain Yukawa-like gravitational potential. The obtained results showed that our estimates for the range of Yukawa interaction Λ at the Solar System scales are in good agreement with recent experimental constrains. Assuming that the estimated value of the range of Λ corresponds to the Compton wavelength of graviton λg, we then estimate the upper bound for its mass mg. We found that these estimates were in agreement with our previous results obtained from the observed stellar orbits around the Galactic Center (GC).