Antarctic krill (Euphausia superba)—one of the most abundant animal species on Earth—exhibits a five to six year population cycle, with oscillations in biomass exceeding one order of magnitude. Previous studies have postulated that the krill cycle is induced by periodic climatological factors, but these postulated drivers neither show consistent agreement, nor are they supported by quantitative models. Here, using data analysis complemented with modelling of krill ontogeny and population dynamics, we identify intraspecific competition for food as the main driver of the krill cycle, while external climatological factors possibly modulate its phase and synchronization over large scales. Our model indicates that the cycle amplitude increases with reduction of krill loss rates. Thus, a decline of apex predators is likely to increase the oscillation amplitude, potentially destabilizing the marine food web, with drastic consequences for the entire Antarctic ecosystem.