Active microrheology was conducted in living cells by applying an optical-trapping force to vigorously-fluctuating tracer beads with feedback-tracking technology. The complex shear viscoelastic modulusG(ω) =G′(ω) –iG″(ω) was measured in HeLa cells in an epithelial-like confluent monolayer. We found thatG(ω) ∝ (−iω)1/2over a wide range of frequencies (1 Hz <ω/2πG(ω) in living cells. On the other hand,G(ω) was found to be dependent on cell metabolism; ATP-depleted cells showed an increased elastic modulusG′(ω) at low frequencies, giving rise to a constant plateau such thatG(ω) =G0+A(−iω)1/2. Both the plateau and the additional frequency dependency ∝ (−iω)1/2of ATP-depleted cells are consistent with a rheological response typical of colloidal jamming. On the other hand, the plateauG0disappeared in ordinary metabolically active cells, implying that living cells fluidize their internal states such that they approach the critical jamming point.Statement of SignificanceIntracellular mechanical properties were measured using optical-trap-based microrheology. Despite expectations to the contrary, shear viscoelasticity was hardly affected by reorganization of cytoskeletal structures during cell-cycle progression (G1 to S and G2 phases), nor by artificial disruption of the actin cytoskeleton induced by chemical inhibitors. Rather, the mechanics of cell interiors is governed by the glassy cytoplasm. Cells depleted of ATP solidified, whereas living cells that maintained metabolic activities were more fluid-like. Instead of a completely fluid response, however, we observed a characteristic power-law viscoelasticityG(ω) ∝ (−iω)1/2over the whole range of frequencies measured. Based on our current understanding of jamming rheology, we discuss how cells fluidize their internal state in a way that pushes the system towards the critical jamming transition.