In 2020 GRAVITY Collaboration detected the Schwarzschild precession in the orbit of S2 star around the supermassive black hole Sgr A*, located at the center of our Galaxy. The orbital precession of the S2 star was parametrized by introducing an ad hoc factor in the parameterized post-Newtonian (PPN) equations of motion, and it was shown that this factor was close to 1, as predicted by the General Relativity (GR). We used this observational fact to constrain the massive gravity theory of Yukawa type and to find new estimates for graviton mass. Since the standard PPN formalism is not viable when dealing with theories that contain massive fields, for this purpose we used the so called extended PPN formalism in which the Newtonian order terms are modified by a non-linear Yukawa-like correction. It is shown that in this way it is possible to further improve our previous constraints on the upper bound of graviton mass.