Imaging techniques using mammographic pictures are the most efficient and straightforward way to diagnose Breast Cancer (BC). The accurate discovery can significantly lower the mortality rate caused by BC. Machine Learning (ML) techniques were utilized for the prediction of BC in images. The ML approaches offered a unique way of making decisions, and they were able to aid the medical expert in providing a second perspective on more precise nodule detection. However, the over-fitting problem in ML degraded the performance of BC detection. To solve this issue, Deep Learning (DL) algorithms were utilized to detect BC early using mammographic images, which is a huge help in detecting BC at an early stage. The Deep Convolutional Neural Networks (DCNN) are being used in DL to help with an accurate BC diagnosis and better BC image outcome detection. However, the time complexity of DCNN is high for a large-scale dataset. In this paper, The DCNN is parallelized in the Mappers of MapReduce (MR) programming model in which the network weights can be iteratively adjusted via determining their fractional gradients following all collections of learning images are propagated throughout the system. Accordingly, the Mapper will parallelize the training phase by distributing the normal, benign, and malignant images that have been preprocessed using the K-Means (KM) algorithm. Each image can be provided to various DCNNs and each DCNN is trained independently in parallel. The output weight of the training stage of DCNNs is aggregated in Reducer and then the weights are then updated for the next iteration. After the completion of the training process, the updated weight is utilized in the all distributed DCNN for classifying the test images of BC. The whole process is termed MapReduce-KM-DCNN (MR-KM-DCNN). Finally, the experimental outcome demonstrates that the proposed MR-KM-DCNN method achieves 88.35 percent accuracy, which is 13.48%, 8.02 %, and 4.85 % higher than the existing SSL-DCNN, AN-DCNN, and KM-DCNN methods. In addition, the running time is reduced by 60% on average compared to previous methods. As a result, it has been verified that the MR-KM-DCNN attained the highest BC detection rate while requiring the smallest amount of computational time.