Bones are bio-composites with biologically tunable mechanical properties, where a polymer matrix of nanofibrillar collagen is reinforced by apatite mineral crystals. Some bones, such as antler, form and change rapidly, while other bone tissues, such as human tooth dentine, develop slowly and maintain constant composition and architecture for entire lifetimes. When studying apatite mineral microarchitecture, mineral distributions or mineralization activity of bone-forming cells, representative samples of tissue are best studied at submicrometre resolution while minimizing sample-preparation damage. Here, we demonstrate the power of ptychographic X-ray tomography to map variations in the mineral content distribution in three dimensions and at the nanometre scale. Using this non-destructive method, we observe nanostructures surrounding hollow tracts that exist in human dentine forming dentinal tubules. We reveal unprecedented quantitative details of the ultrastructure clearly revealing the spatially varying mineralization density. Such information is essential for understanding a variety of natural and therapeutic effects for example in bone tissue healing and ageing.