Single-celled protists use elaborate cytoskeletal structures, including arrays of microtubules at the cell periphery, to maintain polarity and rigidity. The obligate intracellular parasite Toxoplasma gondii has unusually stable cortical microtubules beneath the alveoli, a network of flattened membrane vesicles that subtends the plasmalemma. However, anchoring of microtubules along alveolar membranes is not understood. Here, we show that GAPM1a, an integral membrane protein of the alveoli, plays a role in maintaining microtubule stability. Degradation of GAPM1a causes cortical microtubule disorganisation and subsequent depolymerisation. These changes in the cytoskeleton lead to parasites becoming shorter and rounder, which is accompanied by a decrease in cellular volume. Extended GAPM1a depletion leads to severe defects in division, reminiscent of the effect of disrupting other alveolar proteins. We suggest that GAPM proteins link the cortical microtubules to the alveoli and are required to maintain the shape and rigidity of apicomplexan zoites.