1. Diel migrations (DM; back and forth diel movements along an ecological gradient) undertaken by prey to avoid predators during the day have been demonstrated in many taxa in aquatic ecosystems. In terrestrial ecosystems, prey often shift between various vegetation types whose cover determine their vulnerability (i.e., likelihood of being killed when attacked).
2. We conceptualized that in terrestrial ecosystems, DM could also occur and that the contribution of DM and shifts in vegetation cover use in reducing predation risk should depend upon the predator behaviour and the correlation between encounter risk and vulnerability across vegetation types. We further hypothesized that when the predator distribution is predictable, terrestrial prey could have evolved DM strategies taking them away from the predator when it is active or efficient. 3. We investigated whether plains zebras Equus quagga perform DM in Hwange National Park (Zimbabwe). There, zebras can forage in large patches of open grasslands located near waterholes where they can also easily detect predators. However, they are there at high risk of encountering their main predator, lions Panthera leo, especially at night. 4. We found out that zebras employ a DM anti‐predator strategy. Zebras forage near waterholes during the day but move away from them at sunset, when lions become active. We demonstrated that this DM, occurring over a few kilometres, dramatically reduces their night‐time risk of encountering lions, which generally remain close to waterholes. Zebra changes in night‐time selection for vegetation cover types reduced their risk of encountering lions much less. This may arise from a trade‐off between encounter risk and vulnerability across vegetation types, with zebras favouring low vulnerability once DM has reduced encounter risk. 5. In summary, here we (a) quantify, in a terrestrial system, the effect of a predator‐induced DM on the likelihood of encountering a predator and (b) distinguish the effects of the DM on encounter risk from those related to day/night changes in selection for vegetation types. We discuss how prey partition their risk between encounter risk and habitat‐driven vulnerability and why it is likely critical to understand the emergence of anti‐predator behavioural strategies.