Diffusion-weighted imaging (DWI) is increasingly used to guide the clinical management of patients with breast tumours. However, accurate tumour characterization with DWI and the corresponding apparent diffusion coefficient (ADC) maps are challenging due to their limited resolution. This study aimed to produce super-resolution (SR) ADC images and to assess the clinical utility of these SR images by performing a radiomic analysis for predicting the histologic grade and Ki-67 expression status of breast cancer. To this end, 322 samples of dynamic enhanced magnetic resonance imaging (DCE-MRI) and the corresponding DWI data were collected. A SR generative adversarial (SRGAN) and an enhanced deep SR (EDSR) network along with the bicubic interpolation were utilized to generate SR-ADC images from which radiomic features were extracted. The dataset was randomly separated into a development dataset (n = 222) to establish a deep SR model using DCE-MRI and a validation dataset (n = 100) to improve the resolution of ADC images. This random separation of datasets was performed 10 times, and the results were averaged. The EDSR method was significantly better than the SRGAN and bicubic methods in terms of objective quality criteria. Univariate and multivariate predictive models of radiomic features were established to determine the area under the receiver operating characteristic curve (AUC). Individual features from the tumour SR-ADC images showed a higher performance with the EDSR and SRGAN methods than with the bicubic method and the original images. Multivariate analysis of the collective radiomics showed that the EDSR- and SRGAN-based SR-ADC images performed better than the bicubic method and original images in predicting either Ki-67 expression levels (AUCs of 0.818 and 0.801, respectively) or the tumour grade (AUCs of 0.826 and 0.828, respectively). This work demonstrates that in addition to improving the resolution of ADC images, deep SR networks can also improve tumour image-based diagnosis in breast cancer.