The pressure induced quantum phase transition of the weakly itinerant ferromagnet MnSi isstudied using zero-field 29Si NMR spectroscopy and relaxation. Below P*≈1.2GPa, the intensityof the signal and the nuclear spin-lattice relaxation is independent of pressure, even though theamplitude of the magnetization drops by 20% from the ambient pressure amplitude. For P>P*,the decreasing intensity within the experimentally detectable bandwidth signals the onset of aninhomogeneous phase that persists to the highest pressure measured, P≥1.75GPa, which is wellbeyond the known critical pressure Pc=1.46GPa. Implications for the non-Fermi Liquid behaviorobserved for P>Pc are discussed.