Although CAE has built a strong reputation as a verification, troubleshooting and analysis tool for industrial applications, there is an increasing need for multi-scale multi-physics analysis including new materials and processes, for which current software packages are still missing. Short-fiber-reinforced composites (SFRC) are high-performance engineering materials for lightweight structural applications in the automotive and electronics industries. Typically, SFRC structures are manufactured by injection molding, which induces heterogeneous microstructures, and the resulting nonlinear anisotropic behaviors are challenging to predict by conventional numerical models. In this work, we will introduce a machine learning-based multiscale analysis method by integrating injection molding-induced microstructures, composite material homogenization, and Deep Material Network (DMN) in a commercial finite element simulation software. DMN is a physics-embedded machine learning model that learns the microscale material morphologies hidden in representative volume elements of composites through offline training. By coupling DMN with finite elements, we have developed a highly accurate and efficient data-driven approach, which predicts nonlinear behaviors of composite materials at a computational speed orders-of-magnitude faster than the high-fidelity direct numerical simulation. To model industrial-scale SFRC products, transfer learning is utilized to generate a unified DMN database, which effectively captures the effects of different fiber orientations and volume fractions on the composite mechanical properties. Numerical examples including electronics drop test simulations will be presented to demonstrate the promising performance of this machine learning-based multiscale method.