Computationally efficient and accurate simulations of the flow over axisymmetric bodies of revolution (ABR) have been an important desideratum for engineering design. In this article, the flow field over an ABR is predicted using machine learning (ML) algorithms (e.g., random forest (RF), artificial neural network (ANN), and convolutional neural network (CNN)) using trained ML models as surrogates for classical computational fluid dynamics (CFD) approaches. The data required for the development of the ML models were obtained from high fidelity Reynolds stress transport model (RSTM)-based simulations. The flow field is approximated as functions of x and y coordinates of locations in the flow field and the velocity at the inlet of the computational domain. The optimal hyperparameters of the trained ML models are determined using validation. The trained ML models can predict the flow field rapidly and exhibit orders of magnitude speedup over conventional CFD approaches. The predicted results of pressure, velocity, and turbulence kinetic energy are compared with the baseline CFD data. It is found that the ML-based surrogate model predictions are as accurate as CFD results. This investigation offers a framework for fast and accurate predictions for a flow scenario that is critically important in engineering design.