The instant preheating mechanism in the framework of a scale invariant two measures theory is studied. We introduce this mechanism into a nonoscillating inflationary model as another possible solution to the reheating of the Universe in this theory. In this framework, we consider that the model includes two scalar matter fields, the first is a dilaton field that transforms under scale transformations and will be considered also as the field that drives inflation, and the second is a scalar field that will interact with the inflaton through an effective potential. By assuming this interaction term, we obtain a scenario of instant radiation or decay of particles according to the domain the effective mass of the field that interacts with the inflaton. Also, we consider a scale invariant Yukawa interaction. After performing the transition to the physical Einstein frame, we obtain an expression for the decay rate from our scalar field going into two fermions. Besides, from specific decay rates, different constraints and bounds for the coupling parameters associated with our model are found.