On a global scale, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) poses a serious threat to the health of the human population. Not only humans can be infected, but also their companion animals. The antibody status of 115 cats and 170 dogs, originating from 177 German households known to have been SARS-CoV-2 positive, was determined by enzyme-linked immunosorbent assay (ELISA), and the results were combined with information gathered from a questionnaire that was completed by the owner(s) of the animals. The true seroprevalences of SARS-CoV-2 among cats and dogs were 42.5% (95% CI 33.5–51.9) and 56.8% (95% CI 49.1–64.4), respectively. In a multivariable logistic regression accounting for data clustered in households, for cats, the number of infected humans in the household and an above-average contact intensity turned out to be significant risk factors; contact with humans outside the household was a protective factor. For dogs, on the contrary, contact outside the household was a risk factor, and reduced contact, once the human infection was known, was a significant protective factor. No significant association was found between reported clinical signs in animals and their antibody status, and no spatial clustering of positive test results was identified.