Mechanisms to control cell division are essential for cell proliferation and survival. Bacterial cell growth and division require the coordinated activity of peptidoglycan synthases and hydrolytic enzymes to maintain mechanical integrity of the cell wall. Recent studies suggest that cell separation is governed by mechanical forces. How mechanical forces interact with molecular mechanisms to control bacterial cell division in space and time is poorly understood. Here we use a combination of atomic force microscope imaging, nanomechanical mapping and nanomanipulation to show that enzymatic activity and mechanical forces serve overlapping and essential roles in mycobacterial cell division. We find that mechanical stress gradually accumulates in the cell wall, concentrated at the future division site, culminating in rapid (millisecond) cleavage of nascent sibling cells. Inhibiting cell wall hydrolysis delays cleavage; conversely, locally increasing cell wall stress causes instantaneous and premature cleavage. Cells deficient in peptidoglycan hydrolytic activity fail to locally decrease their cell wall strength and undergo natural cleavage, instead forming chains of non-growing cells. Cleavage of these cells can be mechanically induced by local application of stress with an atomic force microscope. These findings establish a direct link between actively controlled molecular mechanisms and passively controlled mechanical forces in bacterial cell division.