Background: Despite a great deal of existing research on nurses’ job stress and intention to stay, it is still unclear how the association between Chinese nurses’ job stress and intention to stay is affected by presenteeism and family functioning. Aims: This study aimed to investigate the correlations of Chinese nurses’ job stress, presenteeism, and family functioning with their intention to stay and clarify the mediating effect of presenteeism and the moderating effect of family functioning on the association between their job stress and intention to stay. Method: A cross-sectional study of 1,008 nurses was performed in a major general hospital in Qiqihar City, Heilongjiang Province, China. The participants were invited to engage in a questionnaire survey regarding job stress, presenteeism, family functioning, and intention to stay. A moderated mediation analysis was conducted through multiple linear regression analysis and the PROCESS macro. Results: Job stress and presenteeism were negatively correlated with intention to stay, whereas family functioning was positively correlated with intention to stay. The effect of job stress on intention to stay was partially mediated by presenteeism (Effect = −0.147, 95% CI = [−0.305, −0.003]). In addition, family functioning moderated the direct effect of job stress on intention to stay (Index = −0.134, 95% CI = [−0.274, −0.001]). Conclusions: Presenteeism and family functioning were found to play mediating and moderating roles, respectively, in the relationship between job stress and intention to stay. Relevant interventions or family-friendly programs should be developed to enhance nurses’ intention to stay.