Understanding the dynamical behavior of an oscillating bubble near a hydrogel–water interface is an interesting and important multiphase problem arising in many medical treatments including minimizing tissue damage during ultrasound and laser surgeries, guiding targeted drug deliveries, to name a few. Here, by using ultrahigh-speed videography, we captured the complex interaction of an inertial cavitated bubble at a soft hydrogel–water interface penetrating the gel-fluid (water) boundary. Next, we experimentally measured and numerically modeled the nonlinear bubble dynamics near the hydrogel–water interface. Here we present our experimentally observed interface penetration process including annular jetting and shock wave propagation toward the water side. On the gel side we observed the induction of significant large and complex deformations induced by the cavitation bubble. We provide a comprehensive analysis of these phenomena including a quantitative estimate of the associated material strains and damage during this high strain-rate penetration process.