In recent years, the adoption of deep learning (DL) techniques for predicting sea ice concentration (SIC) given both passive microwave (PM) data and reanalysis data has seen a growing interest. For use in downstream services, these SIC estimates should be accompanied by uncertainty estimates. To provide these estimates, we utilize a heteroscedastic Bayesian neural network (HBNN), which can estimate both model (epistemic) and data (aleatoric) uncertainty. We use both PM and atmospheric data as our input features and demonstrate that both are needed for accurate SIC estimates. Results show that, over an annual cycle, the months of melt onset, such as April, May, and June, produce the highest uncertainties relative to other months, with total (epistemic + aleatoric) uncertainties of approximately 20%, while areas in the marginal ice zone contributed highest total uncertainty of 25% spatially. When considering an average over the test year, the level of uncertainty due to the data (aleatoric) is consistent with other studies, at 10%–15%. The advantage of our approach is that the uncertainties are specific to the data instance, and both model and data uncertainties are estimated.