Introduction: Coronavirus disease 2019 (COVID-19) forced Spain to implement unprecedented lockdown restriction. In this context, different factors could worsen sleep quality, but the impact of the pandemic and lockdown on sleep is still mostly unknown. In this cross-sectional study, we describe self-reported sleep disturbances in people without mental health disorders from a large Spanish sample (n = 15,070). Methods: During the early phase of the lockdown (19-26 March), an online survey was launched using a snowball sampling method and included sociodemographic and clinical data along with the Depression, Anxiety, and Stress Scale (DASS-21) and the Impact of Event Scale (IES). Two items of the IES were employed to assess sleep characteristics. Descriptive and bivariate analysis and logistic regression models were performed. Results: Difficulty initiating or maintaining sleep were reported by 23.9% of the sample and was associated in the regression model with age (OR = 1.008, p = .003), female sex (OR = 1.344, p < .001), an income reduction >50% (OR = 1.248, p = .037), having one (OR = 1.208, p = .029) and two or more (OR = 1.299, p = .035) elderly dependents, drinking alcohol (OR = 1.129, p = .024), and a higher score on DASS-21 depression (OR = 1.148, p < .001), anxiety (OR = 1.218, p < .001), or stress (OR = 1.302, p < .001) subscales, whereas being able to enjoy free time (OR = 0.604, p < .001) and painting or listening to music (OR = 0.853, p = .012) were protective factors. Dreams related to COVID-19 were reported by 12.9% of the sample and were associated in the regression model with female sex (OR = 1.617, p < .001), being married (OR = 1.190, p = .015), self-employed (OR = 1.373, p = .032), or a civil servant (OR = 1.412, p = .010), having been tested for COVID-19 (OR = 1.583, p = .012), having infected family or friends (OR = 1.233, p = .001), reading news about coronavirus (OR = 1.139, p = .023), drinking alcohol (OR = 1.251, p < .001), and higher scores on DASS-21 depression (OR = 1.102, p < .001), anxiety (OR = 1.222, p < .001), or stress (OR = 1.213, p < .001) subscales, while protective factors were older age (OR = 0.983, p < .001) and being retired (OR = 0.625, p = .045). Conclusions: These findings could help clinicians and public health systems design and deliver tailored interventions, such as internet-delivered campaigns, to promote sleep quality in the general population.