The extent to which low-frequency (minor allele frequency [MAF] between 1–5%) and rare (MAF ≤ 1%) variants contribute to complex traits and disease in the general population is largely unknown. Bone mineral density (BMD) is highly heritable, is a major predictor of osteoporotic fractures and has been previously associated with common genetic variants^1–8, and rare, population-specific, coding variants⁹. Here we identify novel non-coding genetic variants with large effects on BMD (n_total = 53,236) and fracture (n_total = 508,253) in individuals of European ancestry from the general population. Associations for BMD were derived from whole-genome sequencing (n=2,882 from UK10K), whole-exome sequencing (n= 3,549), deep imputation of genotyped samples using a combined UK10K/1000Genomes reference panel (n=26,534), and de-novo replication genotyping (n= 20,271). We identified a low-frequency non-coding variant near a novel locus, EN1, with an effect size 4-fold larger than the mean of previously reported common variants for lumbar spine BMD⁸ (rs11692564[T], MAF = 1.7%, replication effect size = +0.20 standard deviations [SD], Pmeta = 2×10⁻¹⁴), which was also associated with a decreased risk of fracture (OR = 0.85; P = 2×10⁻¹¹; n_cases = 98,742 and n_controls = 409,511). Using an En1^Cre/flox mouse model, we observed that conditional loss of En1 results in low bone mass, likely as a consequence of high bone turn-over. We also identified a novel low-frequency non-coding variant with large effects on BMD near WNT16 (rs148771817[T], MAF = 1.1%, replication effect size = +0.39 SD, P_meta = 1×10⁻¹¹). In general, there was an excess of association signals arising from deleterious coding and conserved non-coding variants. These findings provide evidence that low-frequency non-coding variants have large effects on BMD and fracture, thereby providing rationale for whole-genome sequencing and improved imputation reference panels to study the genetic architecture of complex traits and disease in the general population.