Breast cancers are evolving, multi-scale systems that are characterized by varied complex spatial structures. In this study, we measured the structural characteristics of 33 breast tumours in patients who were to receive neoadjuvant chemotherapy using dynamic contrast enhanced MRI and fractal geometry. The results showed a significant association between fractal measurements and tumour characteristics. The fractal dimension was associated with receptor status (ER and PR) and the fractal fit was associated with response to chemotherapy, measured using a validated pathological response scale, tumour grade and size. This study describes structure measures that may be a consequence of known prognostic factors during the initial and/or maturation phase of tumour growth. These results suggest that measuring tumour structure in this way can predict an individual's response to neoadjuvant therapy and may identify those who will benefit least from neoadjuvant chemotherapy, allowing alternative treatment options to be selected in those patients.