A novel mechanobiological method is presented to explore qualitatively and quantitatively the inside of living biological cells in three dimensions, paving the way to sense intracellular changes during dynamic cellular processes. For this purpose, holographic optical tweezers, which allow the versatile manipulation of nanoscopic and microscopic particles by means of tailored light fields, are combined with self-interference digital holographic microscopy. This biophotonic holographic workstation enables non-contact, minimally invasive, flexible, high-precision optical manipulation and accurate 3D tracking of probe particles that are incorporated by phagocytosis in cells, while simultaneously quantitatively phase imaging the cell morphology. In a first model experiment, internalized polystyrene microspheres with 1 μm diameter are three-dimensionally moved and tracked in order to quantify distances within the intracellular volume with submicrometer accuracy. Results from investigations on cell swelling provoked by osmotic stimulation demonstrate the homogeneous stretching of the cytoskeleton network, and thus that the proposed method provides a new way for the quantitative 3D analysis of the dynamic intracellular morphology.