Susceptibility to infection such as SARS-CoV-2 may be influenced by host genotype. TwinsUK volunteers (n = 3261) completing the C-19 COVID-19 symptom tracker app allowed classical twin studies of COVID-19 symptoms, including predicted COVID-19, a symptom-based algorithm to predict true infection, derived from app users tested for SARS-CoV-2. We found heritability of 49% (32−64%) for delirium; 34% (20−47%) for diarrhea; 31% (8−52%) for fatigue; 19% (0−38%) for anosmia; 46% (31−60%) for skipped meals and 31% (11−48%) for predicted COVID-19. Heritability estimates were not affected by cohabiting or by social deprivation. The results suggest the importance of host genetics in the risk of clinical manifestations of COVID-19 and provide grounds for planning genome-wide association studies to establish specific genes involved in viral infectivity and the host immune response.