Since March of 2020, billions of people worldwide have been asked to limit their social contacts in an effort to contain the spread of the SARS-CoV-2 virus. However, little research has been carried out to date on the impact of such social distancing measures on the social isolation levels of the population. In this paper, we study the impact of the pandemic on the social isolation of the Spanish population, by means of 32,359 answers to a citizen survey collected over a period of 7 months. We uncover (1) a significant increase in the prevalence of social isolation in the population, reaching almost 26%; (2) gender and age differences, with the largest prevalence of isolation among middle-aged individuals; (3) a strong relationship between economic impact and social isolation; and (4) differences in social isolation, depending on the number of COVID-19 protection measures and on the perception of coronavirus infection risk by our participants. Our research sheds quantitative light on the sociological impact of the pandemic, and enables us to identify key factors in the interplay between the deployment of non-pharmaceutical interventions to contain the spread of an infectious disease and a population’s levels of social isolation.