In this paper, we study the quenching behaviour for a system of two reaction–diffusion equations arising in the modelling of the spatio-temporal interaction of prey and predator populations in fragile environment. We first provide some sufficient conditions on the initial data to have finite time quenching. Then we classify the initial data to distinguish type I quenching and type II quenching, by introducing a delicate energy functional along with the help of some a priori estimates. Finally, we present some results on the quenching set. It can be a singleton, the whole domain, or a compact subset of the domain.