The incorporation of multi-omics data sources, including gene expression profiles, copy number variations, genetic mutations, and protein phosphorylation levels can significantly improve model classification disease accuracy. This paper presents a Deep Neural Network (DNN) architecture with feature selection mechanism to detect the breast cancer using multi-omics data. A hybrid feature selection approach by integrating Mutual Information and Recursive Feature Elimination (RFE) is employed to determine the relevant feature for handling high-dimensional data. To address class imbalance problem, the Synthetic Minority Oversampling Technique (SMOTE) and weighted class methods are used in the paper. DNN model contains 4 hidden layers and batch normalization and dropout layers to reduce over fitting and to improve generalization ability. The model training is carried out using stratified k-fold cross-validation and early stopping. The model is evaluated on a balanced test data set of 245 samples and was able to achieve an overall classification accuracy of 93.06%, with a precision of 89.47%, recall of 97.54, F1-score of 93.33, and AUC of 93.08. The model performed well overall with respect to recall in order to reduce missed diagnoses and there is an indication of operational capacity for clinical utility, however lower precision suggests some errors in false positives; incorporating multi-omics data with the deep learning model demonstrated capability for disease classification and also for optimizing feature selection for improved predictive capabilities.