We report the radio observations of the eclipsing black widow pulsar J1720−0534, a 3.26 ms pulsar in orbit with a low mass companion of mass 0.029 to 0.034 M⊙. We obtain the phase-connected timing ephemeris and polarization profile of this millisecond pulsar (MSP) using the Five-hundred-meter Aperture Spherical radio Telescope (FAST), the Green Bank Telescope (GBT), and the Parkes Telescope. For the first time from such a system, an oscillatory polarization angle change was observed from a particular eclipse egress with partial depolarization, indicating 10-milliGauss-level reciprocating magnetic fields oscillating in a length scale of 5 × 103 km (assuming an orbital inclination angle of 90°) outside the companion's magnetosphere. The dispersion measure variation observed during the ingresses and egresses shows the rapid raising of the electron density in the shock boundary between the companion's magnetosphere and the surrounding pulsar wind. We suggest that the observed oscillatory magnetic fields originate from the pulsar wind outside the companion's magnetosphere.