The COVID-19 pandemic caused lifestyle changes, with unknown effect on pets’ quality of life (QoL). Between May and July 2020, we distributed an online survey to investigate the role of several factors on feline and canine QoL, including lockdown-related factors. We used existing scales to measure human and pets’ personalities (Reinforcement Sensitivity Theory Personality Questionnaire, RST-PQ; RST-Dog; RST-Cat) and the human–animal relationship (Lexington Attachment to Pets Scale, LAPS) and the Milan Pet Quality of Life instrument (MPQL). Overall, 235 participants reported about 242 adult pets (Ncats = 78, Ndogs = 164). Factor analysis confirmed the structure and internal reliability of the existing scales (RST-PQ, RST-Dog, RST-Cat, LAPS) and suggested a four-factor structure for the MPQL (physical, psychological, social, environmental). The results indicate that the pets’ psysical QoL was largely explained by pet-related elements (pets’ demographics and life experience, and pets’ personality). Conversely, the pets’ psychological QoL was explained mostly by owner-related elements, such as the owners’ demographics, COVID-19-related changes, and the owners’ personality. Predictably, the pets’ environmental QoL is mostly explained by environmental factors, such as the outdoor access in the home environment and the country. Finally, the pets’ social QoL was explained by the larger combination of models: pets’ characteristics and personality, environment and COVID-19-related changes, and the pet–human relationship. These findings can be explained by two non-mutually exclusive mechanisms. The reported changes may be a by-product of the COVID-19 pandemic’s psychological and lifestyle effects on the owners, which in turn alter the way the owners interact with their pets and look after them. However, the owners’ characteristics and mood may bias their answers regarding their pets.