The disease produced by the severe acute respiratory syndrome‐related coronavirus 2 (SARS‐CoV‐2) is currently one of the primary concerns worldwide. Knowing the zoonotic origin of the disease and that several animal species, including dogs and cats, are susceptible to viral infection, it is critical to assess the relevance of pets in this pandemic. Here, we performed a large‐scale study on SARS‐CoV‐2 serological and viral prevalence in cats and dogs in Spain in order to elucidate their role and susceptibility. Samples from animals in contact with COVID‐19 positive people and/or compatible symptoms (n = 492), as well as from random animals (n = 1024), were taken. Despite the large number of animals analyzed, only 12 animals (eight dogs and four cats), which represents 0.79% of the total analyzed animals (n = 1516), were positive for viral SARS‐CoV‐2 RNA detection by reverse transcription quantitative PCR (RT‐qPCR) in which viral isolation was possible in four animals. We detected neutralizing antibodies in 34 animals, four of them were also positive for PCR. This study evidences that pets are susceptible to SARS‐CoV‐2 infection in natural conditions but at a low level, as evidenced by the low percentage of positive animals detected, being infected humans the main source of infection. However, the inclusion of animals in the surveillance of COVID‐19 is still recommended.