Complete tensor-scalar and hydrodynamic equations are presented and integrated, for a self-gravitating perfect fluid, in order to follow the gravitational collapse (including full hydrodynamics) of a neutron star and to study the resulting scalar gravitational wave. During the collapse, only a part of the scalar energy is radiated away as monopolar wave. This wave could be detected by a laser interferometric gravitational wave observatory (such as VIRGO or LIGO), thus constraining the parameters of the theory. The dependence of the wave amplitude and the radiated energy on those parameters is studied and it is shown that there exists some critical value of the parameter of the coupling function between the tensor and the scalar fileds, above which these quantities dramatically increase.