An apparatus for manufacturing an interior part of a vehicle may include a pressure sensor disposed at a position on a surface of a base of the interior part at which a foaming pressure of a foam material is detected, a tube controlling an expanding pressure, disposed on a surface of a skin layer of the interior part to press against the base, and a tube pressure controller for controlling the expanding pressure of the tube, which causes the skin layer to be pressed to the surface of the base, relative to the foaming pressure of the foam material detected by the pressure sensor during foaming of the foam material, to block leakage of the foam material.