The viscosity of nanofluids can be influenced by many physical factors so it is difficult to obtain an accurate prediction model using only traditional theoretical model-driven methods or data-driven black-box models. This study proposes a modern approach named Physics Guided Deep Neural Network (PGDNN) for viscosity prediction that combines the data-driven models and physics-based theoretical models to achieve their complementary strengths and develop the modeling of physical processes. This PGDNN model is applied with a large number of data points (9000 data points) containing both experimental and simulated data of spherical nanoparticles Al2O3, CuO, SiO2, and TiO2. Further, this technique overcomes the overfitting issue and performs better than other traditional models while predicting unseen data. As far as we know, the PGDNN model is novel and not even used earlier to predict the viscosity of nanofluids. The learning performance of the proposed model is analyzed using different statistical performance indicators and Bayesian optimization is used for hyper-parameter tuning. Then, epistemic uncertainty quantification is performed to estimate the confidence level of the proposed model. Our PGDNN model outperformed various previous theoretical and computer-aided models with R-2=0.9961 and RMSE = 0.0312. Moreover, a sensitivity analysis is performed and the results show that the volume fraction of particle is the most and viscosity of a base fluid is the second most significant parameters to determine the viscosity of nanofluids.