We report the detection of a curved magnetic field in the ring-like shell of the bubble N4, derived from near-infrared polarization of reddened diskless stars located behind this bubble. The magnetic field in the shell is curved and parallel to the ring-like shell, and its strength is estimated to be similar to 120 mu G in the plane of the sky. The magnetic field strength in the shell is significantly enhanced compared to the local field strength. We calculate the mass-to-flux ratio for the submillimeter clumps in the shell and find that they are all magnetically subcritical. Our results demonstrate that the magnetic field strengthens as the interstellar medium is compressed into a shell, and suggest that the magnetic field has the potential to hinder star formation triggered by H II region expansion.