The HIV-1 reservoir is the major hurdle to curing HIV-1. However, the impact of the viral genome on the HIV-1 reservoir, i.e. its heritability, remains unknown. We investigate the heritability of the HIV-1 reservoir size and its long-term decay by analyzing the distribution of those traits on viral phylogenies from both partial-pol and viral near full-length genome sequences. We use a unique nationwide cohort of 610 well-characterized HIV-1 subtype-B infected individuals on suppressive ART for a median of 5.4 years. We find that a moderate but significant fraction of the HIV-1 reservoir size 1.5 years after the initiation of ART is explained by genetic factors. At the same time, we find more tentative evidence for the heritability of the long-term HIV-1 reservoir decay. Our findings indicate that viral genetic factors contribute to the HIV-1 reservoir size and hence the infecting HIV-1 strain may affect individual patients' hurdle towards a cure.