The development of set-based genetic-survival association tests has been focusing on right-censored survival outcomes. However, interval-censored failure time data arise widely from health science studies, especially those on the development of chronic diseases. In this paper, we proposed a suite of set-based genetic association and interaction tests for interval-censored survival outcomes under a unified weighted-V-statistic framework. Besides dealing with interval censoring, the new tests can account for genetic effect heterogeneity and accommodate left truncation of survival outcomes. Simulation studies showed that the new tests perform well in terms of size and power under various scenarios and that the new interaction test is more powerful than the standard likelihood ratio test for testing gene–gene/gene–environment interactions. The practical utility of the developed tests was illustrated by a genome-wide association study of age to early childhood caries.