Structural oscillations and solvation dynamics in the mitochondria of a live cell are studied by time-resolved microscopy using a covalent fluorescence probe. We compared the dynamics in a human breast cancer cell (MCF-7) with that in a normal breast cell MCF-10A. The probe, CPM (7-diethylamino-3-(4-maleimido-phenyl)-4-methylcoumarin), binds with the free thiol groups. In MCF-10A cell, CPM binds with the discrete mitochondria. In MCF-7, CPM labels the clustered mitochondria in the peri-nuclear region. Location of the CPM in the mitochondria is confirmed by colocalization with a mitochondria-tracker dye. The red-ox cycle in the mitochondria causes periodic fluctuation in the microenvironment in the discrete mitochondria. This is manifested in fluctuations in fluorescence intensity of CPM bound to mitochondria. The magnitude of oscillation is much less for CPM bound to the clustered mitochondria (in which the red-ox cycle is inefficient) in the cancer cell (MCF-7). In both of the cells (MCF-10A and MCF-7) CPM bound to thiol-containing proteins in mitochondria exhibits ultraslow response with average solvation time (⟨τs⟩) of 850 and 1400 ps in MCF-10A and MCF-7, respectively.