This work aims to find out the effectiveness of sources based on Big Data like mobile phone records to analyze mobility flows and changes in the population of Spain in different scenarios during the period of the pandemic caused by the COVID-19 virus. To this end, we have used mobile phone data provided by the National Institute of Statistics from four days corresponding to different phases of the pandemic. Origin–Destination matrices and population estimation calculations at the spatial level of population cells have been elaborated. The results show different patterns that correspond to the phenomena that have occurred, as the decrease of the population during the periods associated with the confinement measures. The consistency of findings with the reality and the generally good correlation with the population census data indicate that mobile phone records are a useful source of data for the elaboration of demographic and mobility studies during pandemics.