Several scenarios for binary star formation have been proposed: disk fragmentation, turbulent fragmentation, and mixed scenario. The recent Gaia observation suggests that the disk fragmentation mechanism contributes to the formation of the binary systems in the wide ranges of binary parameters: masses and separations of binary stars. However, the formation mechanism of a binary star with a small separation in a disk fragmentation scenario is not well understood. We performed three-dimensional MHD simulations to investigate the interaction between binary stars, a circumbinary disk, and an infalling envelope. Fixed mesh refinement is utilized to increase a spatial resolution around the binary stars. The simulations show that the initially assumed vertical magnetic field reproduces a fast outflow from the circumstellar disk around each star and a slow outflow from the circumstellar disk. The magnetic field also excites turbulence due to magneto-rotational instability in the circumbinary disk. These magnetic effects transfer angular momentum from the central region of the system, resulting in a decrease in the binary separation where the magnetic field strength is stronger than a certain threshold.