The discovery of important biomarkers is a significant step towards understanding the molecular mechanisms of carcinogenesis; enabling accurate diagnosis for, and prognosis of, a certain cancer type. Before recommending any diagnosis, genomics data such as gene expressions (GE) and clinical outcomes need to be analyzed. However, complex nature, high dimensionality, and heterogeneity in genomics data make the overall analysis challenging. Convolutional neural networks (CNN) have shown tremendous success in solving such problems. However, neural network models are perceived mostly as 'black box' methods because of their not well-understood internal functioning. However, interpretability is important to provide insights on why a given cancer case has a certain type. Besides, finding the most important biomarkers can help in recommending more accurate treatments and drug repositioning. Moreover, the 'right to explanation' of the EU GDPR gives patients the right to know why and how an algorithm made a diagnosis decision. Hence, in this paper, we propose a new approach called OncoNetExplainer to make explainable predictions of cancer types based on GE data. We used genomics data about 9,074 cancer patients covering 33 different cancer types from the Pan-Cancer Atlas on which we trained CNN and VGG16 networks using guided-gradient class activation maps++ (GradCAM++). Further, we generate class-specific heat maps to identify significant biomarkers and computed feature importance in terms of mean absolute impact to rank top genes across all the cancer types. Quantitative and qualitative analyses show that both models exhibit high confidence at predicting the cancer types correctly giving an average precision of 96.25%. To provide comparisons with the baselines, we identified top genes, and cancer-specific driver genes using gradient boosted trees and SHapley Additive ex-Planations (SHAP). Finally, our findings were validated with the annotations provided by the TumorPortal.