The study analyzed the association of the fear of contagion for oneself and for family members (FMs) during the first wave of the COVID-19 pandemic, with demographic and socioeconomic status (SES) and health factors. The study was performed within the EPICOVID19 web-based Italian survey, involving adults from April–June 2020. Out of 207,341 respondents, 95.9% completed the questionnaire (60% women with an average age of 47.3 vs. 48.9 years among men). The association between fear and demographic and SES characteristics, contacts with COVID-19 cases, nasopharyngeal swab, self-perceived health, flu vaccination, chronic diseases and specific symptoms was analyzed by logistic regression model; odds ratios adjusted for sex, age, education and occupation were calculated (aORs). Fear for FMs prevailed over fear for oneself and was higher among women than men. Fear for oneself decreased with higher levels of education and in those who perceived good health. Among those vaccinated for the flu, 40.8% responded they had feelings of fear for themselves vs. 34.2% of the not vaccinated. Fear increased when diseases were declared and it was higher when associated with symptoms such as chest pain, olfactory/taste disorders, heart palpitations (aORs > 1.5), lung or kidney diseases, hypertension, depression and/or anxiety. Trends in fear by region showed the highest percentage of positive responses in the southern regions. The knowledge gained from these results should be used to produce tailored messages and shared public health decisions.