Germline copy number variants (CNVs) are pervasive in the human genome but potential disease associations with rare CNVs have not been comprehensively assessed in large datasets. We analysed rare CNVs in genes and non-coding regions for 86,788 breast cancer cases and 76,122 controls of European ancestry with genome-wide array data. Gene burden tests detected the strongest association for deletions in BRCA1 (P = 3.7E-18). Nine other genes were associated with a p-value < 0.01 including known susceptibility genes CHEK2 (P = 0.0008), ATM (P = 0.002) and BRCA2 (P = 0.008). Outside the known genes we detected associations with p-values < 0.001 for either overall or subtype-specific breast cancer at nine deletion regions and four duplication regions. Three of the deletion regions were in established common susceptibility loci. To the best of our knowledge, this is the first genome-wide analysis of rare CNVs in a large breast cancer case-control dataset. We detected associations with exonic deletions in established breast cancer susceptibility genes. We also detected suggestive associations with non-coding CNVs in known and novel loci with large effects sizes. Larger sample sizes will be required to reach robust levels of statistical significance.