The restrictive measures implemented to stem the spread of COVID-19 abruptly changed the lives of many cats and their owners. This study explored whether the lockdown in Italy affected the cat–owner relationship, as well as cat behaviour and welfare. A survey that included questions on owner and cat’s demographics, living environment, cat behaviour and a modified version of the Cat/Dog Relationship Scale (C/DORS) was distributed online during the lockdown and was completed by 548 cat owners, mainly women (81.6%). With regard to the C/DORS subscales, both emotional closeness and cat–owner interactions increased during confinement, as opposed to a reduction in perceived costs. The effect of the type of job, family role and owner’s age on the C/DORS scores suggests that the relationship improved for those owners that, due to the lockdown, increased the time spent with their cats. For 58.8% of respondents, their cat’s general behaviour did not change, but when changes occurred, they were mostly positive (20.4%). Attention-seeking and demanding behaviours were the most increased during lockdown (25.7%). Cats with pre-existing problematic behaviours tended to either remain stable or improve during confinement. The overall positive effects of lockdown-related environmental changes on a cat’s behaviour suggest that some aspects of commonly implemented cat management practices should be revised to improve cat welfare in normal circumstances.