The advent of implantable bioelectronic devices offers prospective solutions toward health monitoring and disease diagnosis and treatments. However, advances in power modules have lagged far behind the tissue-integrated sensor nodes and circuit units. Here, we report a soft implantable power system that monolithically integrates wireless energy transmission and storage modules. The energy storage unit comprises biodegradable Zn-ion hybrid supercapacitors that use molybdenum sulfide (MoS2) nanosheets as cathode, ion-crosslinked alginate gel as electrolyte, and zinc foil as anode, achieving high capacitance (93.5 mF cm-2) and output voltage (1.3 V). Systematic investigations have been conducted to elucidate the charge storage mechanism of the supercapacitor and to assess the biodegradability and biocompatibility of the materials. Furthermore, the wirelessly transmitted energy can not only supply power directly to applications but also charge supercapacitors to ensure a constant, reliable power output. Its power supply capabilities have also been successfully demonstrated for controlled drug delivery.