Bio-integrated devices need power sources to operate. Despite widely used technologies that can provide power to large-scale targets, such as wired energy supplies from batteries or wireless energy transduction, a need to efficiently stimulate cells and tissues on the microscale is still pressing. The ideal miniaturized power source should be biocompatible, mechanically flexible and able to generate an ionic current for biological stimulation, instead of using electron flow as in conventional electronic devices. One approach is to use soft power sources inspired by the electrical eel; however, power sources that combine the required capabilities have not yet been produced, because it is challenging to obtain miniaturized units that both conserve contained energy before usage and are easily triggered to produce an energy output. Here we develop a miniaturized soft power source by depositing lipid-supported networks of nanolitre hydrogel droplets that use internal ion gradients to generate energy. Compared to the original eel-inspired design, our approach can shrink the volume of a power unit by more than 10-fold and it can store energy for longer than 24 h, enabling operation on-demand with a 680-fold greater power density of about 1,300 W m. Our droplet device can serve as a biocompatible and biological ionic current source to modulate neuronal network activity in three-dimensional neural microtissues and in ex vivo mouse brain slices. Ultimately, our soft microscale ionotronic device might be integrated into living organisms.