There is considerable controversy about swift heavy ion (SHI) irradiation induced displacive phase transitions in thermally insulating oxides. We present here unambiguous evidence for tetragonal to monoclinic and rhombohedral to monoclinic phase transitions in BaTiO3 under swift heavy ion irradiation (120MeV 108Ag+9 ions) using in-situ x-ray powder diffraction (XRPD) studies. The anomalous splitting/broadening of 111/222pc, 200pc and 220pc pseudocubic peaks for fluences greater than 3*1012 ions/cm2 reveal structural changes before amorphization at higher fluences. Lebail analysis of XRPD profiles confirm that the monoclinic phase is of MA type in the Cm space group. Shear stress for the structural phase transition is estimated to be ~ 430MPa, which we believe is generated as a result of stopping of the SHI.