The COVID-19 pandemic has been spreading rapidly in Spain. The objective of this work was to examine the psychological impact of the pandemic and the Spanish national quarantine that took place during March and April 2020. We investigated the prevalence of fear of coronavirus, emotional symptoms and sleep problems. We also examined possible positive effects. A sample of 1,161 participants (aged 19 to 84 years) completed online the Coronavirus Psychological Impact Questionnaire, the Intolerance of Uncertainty Scale–12, and the Positive and Negative Affect Schedule. Results indicated that the most common fears pertain to the domains of contagion/disease/death, social isolation, and employment/income issues. We found high levels of emotional impact reflected in fear of coronavirus, sleep problems, and emotional symptoms (preoccupation, distress, hopelessness, depression, anxiety, nervousness, and restlessness). Regression analyses revealed that intolerance of uncertainty and social media exposure are strong predictors of the impact. We also found some effects of the COVID-19 lockdown favoring positive personal experiences. A new self-report instrument to assess psychological impact of coronavirus is provided.