The capability to directly interrogate intracellular structures inside a single cell for measurement and manipulation is important for understanding subcellular and suborganelle activities, diagnosing diseases, and developing new therapeutic approaches. Compared with measurements of single cells, physical measurement and manipulation of subcellular structures and organelles remain underexplored. To improve intracellular physical measurement and manipulation, we have developed a multipole magnetic tweezers system for micromanipulation involving submicrometer position control and piconewton force control of a submicrometer magnetic bead inside a single cell for measurement in different locations (spatial) and different time points (temporal). The bead was three-dimensionally positioned in the cell using a generalized predictive controller that addresses the control challenge caused by the low bandwidth of visual feedback from high-resolution confocal imaging. The average positioning error was quantified to be 0.4 μm, slightly larger than the Brownian motion-imposed constraint (0.31 μm). The system is also capable of applying a force up to 60 pN with a resolution of 4 pN for a period of time longer than 30 min. The measurement results revealed that significantly higher stiffness exists in the nucleus' major axis than in the minor axis. This stiffness polarity is likely attributed to the aligned actin filament. We also showed that the nucleus stiffens upon the application of an intracellularly applied force, which can be attributed to the response of structural protein lamin A/C and the intracellular stress fiber actin filaments.