Inelastic neutron scattering and bulk magnetic susceptibility studies of the quantum S=1/2 spin ladder system IPA-CuCl3 are performed under hydrostatic pressure. The pressure dependence of the spin gap $Delta$ is determined. At $P=1.5$ GPa it is reduced to $Delta=0.79$ meV from $Delta=1.17$ meV at ambient pressure. The results allow us to predict a soft-mode quantum phase transition in this system at P$_mathrm{c}sim 4$ GPa. The measurements are complicated by a proximity of a structural phase transition that leads to a deterioration of the sample.
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