Microscale organisms and specialized motile cells use protein-based spring-like responsive structures to sense, grasp and move. Rendering this biomechanical transduction functionality in an artificial micromachine for applications in single-cell manipulations is challenging due to the need for a bio-applicable nanoscale spring system with a large and programmable strain response to piconewton-scale forces. Here we present three-dimensional nanofabrication and monolithic integration, based on an acrylic elastomer photoresist, of a magnetic spring system with quantifiable compliance sensitive to 0.5 pN, constructed with customized elasticity and magnetization distributions at the nanoscale. We demonstrate the effective design programmability of these 'picospring' ensembles as energy transduction mechanisms for the integrated construction of customized soft micromachines, with onboard sensing and actuation functions at the single-cell scale for microrobotic grasping and locomotion. The integration of active soft springs into three-dimensional nanofabrication offers an avenue to create biocompatible soft microrobots for non-disruptive interactions with biological entities.