We report the discovery of an anomalous flare in a bright blazar, namely, PKS 0208-512, one of the targets of the Yale/SMARTS optical-near-infrared (OIR) monitoring program of Fermi blazars. We identify three intervals during which PKS 0208-512 undergoes outbursts at OIR wavelengths lasting for longer than 3 months. Its brightness increases and then decreases again by at least 1 magnitude in these intervals. In contrast, the source undergoes bright phases in GeV energies lasting for longer than 1 month during intervals 1 and 3 only. The OIR outburst during interval 2 is comparable in brightness and temporal extent to the OIR flares during intervals 1 and 3 which do have gamma-ray counterparts. By analyzing the gamma-ray, OIR, and supporting multi-wavelength variability data in details, we speculate that the OIR outburst during interval 2 was caused by a change in the magnetic field without any change in the total number of emitting electrons or Doppler factor of the emitting region. Alternatively, it is possible that the location of the outburst in the jet during interval 2 was closer to the black hole where the jet is more compact and the bulk Lorentz factor of the material in the jet is smaller. We also discuss the complex OIR spectral behavior during these three intervals.