Premature ovarian insufficiency (POI) affects 1% of women and is a leading cause of infertility. It is often considered to be a monogenic disorder, with pathogenic variants in ~100 genes described in the literature. We sought to systematically evaluate the penetrance of variants in these genes using exome sequence data in 104,733 women from the UK Biobank, 2,231 (1.14%) of whom reported natural menopause under the age of 40. In the largest study of POI to date, we found limited evidence to support any previously reported autosomal dominant effect. For nearly all heterozygous effects on previously reported POI genes we were able to rule out even modest penetrance, with 99.9% (13,699/13,708) of all identified protein truncating variants found in reproductively healthy women. We found evidence of novel haploinsufficiency effects in several genes, including TWNK (1.54 years earlier menopause, P=1.59*10-6) and SOHLH2 (3.48 years earlier menopause, P=1.03*10-4). Collectively our results suggest that for the vast majority of women, POI is not caused by autosomal dominant variants either in genes previously reported or currently evaluated in clinical diagnostic panels. We suggest that the majority of POI cases are likely oligogenic or polygenic in nature, which has major implications for future clinical genetic studies, and genetic counselling for families affected by POI.