The age of menopause is associated with fertility and disease risk, and its genetic control is of great interest. We used whole-exome sequences from 119,992 women in the UK Biobank to test for associations between rare damaging variants and age at natural menopause. Rare damaging variants in three genes significantly associated with menopause: CHEK2 (p = 6.2 × 10-51) and DCLRE1A (p = 1.2 × 10-12) with later menopause and TOP3A (p = 8.8 × 10-8) with earlier menopause. Two additional genes were suggestive: RAD54L (p = 2.3 × 10-6) with later menopause and HROB (p = 2.7 × 10-6) with earlier menopause. In a follow-up analysis of repeated questionnaires in women who were initially pre-menopausal, CHEK2, TOP3A, and RAD54L genotype associated with subsequent menopause. Consistent with previous GWAS, all five genes are involved in the DNA-damage repair pathway. Phenome-wide scans across 363,977 men and women revealed that in addition to known associations with cancers and blood cell counts, rare variants in CHEK2 also associated with increased risk of uterine fibroids, polycystic ovary syndrome, and prostate hypertrophy; these associations are not shared with higher-penetrance breast cancer genes. Causal mediation analysis suggests that approximately 8% of the breast cancer risk conferred by CHEK2 pathogenic variants after menopause is mediated through delayed menopause.