Rubber hand illusion (RHI) refers to the illusory sense of body ownership of a fake hand, which is induced by synchronous visuotactile stimulation to the real and fake hands. A negative correlation was reported between the cardiac interoception and the strength of RHI, but the subsequent studies have been unsuccessful in replicating it. On the other hand, voluntary action is suggested to link interoception and the sense of body ownership in different situations. If so, moving RHI, induced by the active or the passive finger tapping while observing a fake hand, might reveal the relationship more clearly. The measurement of interoception has been another issue. We, therefore, examined the relationship between the moving RHI and two measures of interoception: interoceptive accuracy (IAcc) measured by the conventional heartbeat counting task and interoceptive sensibility (IS) measured using a questionnaire. For the classical visuotactile RHI, our results supported the lack of association between the interoception measures and RHI. For the moving RHI, a stronger sense of body ownership was induced for participants with higher IS regardless of active or passive movement, and a stronger sense of agency was caused by active than passive movement only for those with lower IAcc. These results reveal the dynamic links between the interoception and the bodily senses. The results also suggest that multiple dimensions of interoception affect the bodily senses differently.