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 mainly unknown. Bone mineral density (BMD) is highly heritable, a major predictor of osteoporotic fractures, and has been previously associated with common genetic variants, as well as rare, population‐specific, coding variants. Here we identify novel non‐coding genetic variants with large effects on BMD (ntotal = 53,236) and fracture (ntotal = 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 (ref. 10); a population‐based genome sequencing consortium), whole‐exome sequencing (n = 3,549), deep imputation of genotyped samples using a combined UK10K/1000 Genomes 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 fourfold larger than the mean of previously reported common variants for lumbar spine BMD (rs11692564(T), MAF = 1.6%, replication effect size = +0.20 s.d., Pmeta = 2 × 10−14), which was also associated with a decreased risk of fracture (odds ratio = 0.85; P = 2 × 10−11; ncases = 98,742 and ncontrols = 409,511). Using an En1cre/flox mouse model, we observed that conditional loss of En1 results in low bone mass, probably as a consequence of high bone turnover. We also identified a novel low‐frequency non‐coding variant with large effects on BMD near WNT16 (rs148771817(T), MAF = 1.2%, replication effect size = +0.41 s.d., Pmeta = 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.