Severe malaria occurs predominantly in young children and immunity to clinical disease is associated with cumulative exposure in holoendemic settings. The relative contribution of immunity against various stages of the parasite life cycle that results in controlling infection and limiting disease is not well understood. Here we analyse the dynamics of Plasmodium falciparum malaria infection after treatment in a cohort of 197 healthy study participants of different ages in order to model naturally acquired immunity. We find that both delayed time-to-infection and reductions in asymptomatic parasitaemias in older age groups can be explained by immunity that reduces the growth of blood stage as opposed to liver stage parasites. We found that this mechanism would require at least two components - a rapidly acting strain-specific component, as well as a slowly acquired cross-reactive or general immunity to all strains. Analysis and modelling of malaria infection dynamics and naturally acquired immunity with age provides important insights into what mechanisms of immune control may be harnessed by malaria vaccine strategists.