A parallel adaptive mesh refinement (AMR) finite‐volume scheme for predicting ideal MHD flows is used to simulate the initiation, structure, and evolution of a coronal mass ejection (CME) and its interaction with the magnetosphere‐ionosphere system. The simulated CME is driven by a local plasma density enhancement on the solar surface with the background initial state of the corona and solar wind represented by a newly devised “steady state” solution. The initial solution has been constructed to provide a reasonable description of the time‐averaged solar wind for conditions near solar minimum: (1) the computed magnetic field near the Sun possesses high‐latitude polar coronal holes, closed magnetic field flux tubes at low latitudes, and a helmet streamer structure with a neutral line and current sheet; (2) the Archimedean spiral topology of the interplanetary magnetic field is reproduced; (3) the observed two‐state nature of the solar wind is also reproduced with the simulation yielding fast and slow solar wind streams at high and low latitudes, respectively; and (4) the predicted solar wind plasma properties at 1 AU are consistent with observations. Starting with the generation of a CME at the Sun, the simulation follows the evolution of the solar wind disturbance as it evolves into a magnetic cloud and travels through interplanetary space and subsequently interacts with the terrestrial magnetosphere‐ionosphere system. The density‐driven CME exhibits a two‐step release process, with the front of the CME rapidly accelerating following the disruption of the near‐Sun closed magnetic field line structure and then moving at a nearly constant speed of ∼560 km/s through interplanetary space. The CME also produces a large magnetic cloud (> 100 RS across) characterized by a magnetic field that smoothly rotates northward and then back again over a period of ∼2 days at 1 AU. The cloud does not contain a sustained period with a strong southward component of the magnetic field, and, as a consequence, the simulated CME is somewhat ineffective in generating strong geo‐magnetic activity at Earth. Nevertheless, the simulation results illustrate the potential, as well as current limitations, of the MHD‐based space weather model for enhancing the understanding of coronal physics, solar wind plasma processes, magnetospheric physics, and space weather phenomena. Such models will provide the foundation for future, more comprehensive space weather prediction tools.