The presence of diffuse morphogen gradients in tissues supports a view in which growth is locally homogenous. Here we challenge this view: we used a high-resolution quantitative approach to reveal significant growth variability among neighboring cells in the shoot apical meristem, the plant stem cell niche. This variability was strongly decreased in a mutant impaired in the microtubule-severing protein katanin. Major shape defects in the mutant could be related to a local decrease in growth heterogeneity. We show that katanin is required for the cell's competence to respond to the mechanical forces generated by growth. This provides the basis for a model in which microtubule dynamics allow the cell to respond efficiently to mechanical forces. This in turn can amplify local growth-rate gradients, yielding more heterogeneous growth and supporting morphogenesis.