We present a method for analysing mobile phone call detail records to identify individuals whom we believe to be have been internally displaced as a result of a sudden-onset disaster. We model each anonymous individual's movements trajectory as a piecewise-constant time series signal, assume that a disaster-induced displacement is exhibited as a level shift from an individual's 'normal' location, and then apply a step detection algorithm to identify level shifts in the signal. In contrast to typical methods that are used to analyse mobility patterns from call detail records, where the aggregate movements of large groups of individuals are analysed, our method offers the advantage that no assumptions regarding the destination or duration of an individual's displacement are necessary. We have applied the method to the datasets from three disasters - the 2010 earthquake in Haiti, the 2015 Gorkha earthquake in Nepal, and Hurricane Matthew in Haiti in 2016. Our results demonstrate that this method can facilitate improvements in the analysis and modelling of the mobility of internally displaced persons in post-disaster scenarios, using call detail records. Such analyses can be used to complement traditional survey methods to assess the scale and characteristics of disaster-induced displacements in a timely manner.