Contractile actomyosin networks generate forces that drive tissue morphogenesis. Actomyosin contractility is controlled primarily by reversible phosphorylation of the myosin-II regulatory light chain through the action of myosin kinases and phosphatases. While the role of myosin light-chain kinase in regulating contractility during morphogenesis has been largely characterized, there is surprisingly little information on myosin light-chain phosphatase (MLCP) function in this context. Here, we use live imaging of Drosophila follicle cells combined with mathematical modelling to demonstrate that the MLCP subunit flapwing (flw) is a key regulator of basal myosin oscillations and cell contractions underlying egg chamber elongation. Flw expression decreases specifically on the basal side of follicle cells at the onset of contraction and flw controls the initiation and periodicity of basal actomyosin oscillations. Contrary to previous reports, basal F-actin pulsates similarly to myosin. Finally, we propose a quantitative model in which periodic basal actomyosin oscillations arise in a cell-autonomous fashion from intrinsic properties of motor assemblies.