We perform monthly monitoring of the quasar 1633+382 (4C+38.41) within a sample of gamma-ray blazars with the VLBA at 43 GHz along with optical photometric and polarimetric observations. We construct the gamma-ray light curve of 1633+382 using data obtained by the Fermi LAT. We find that a high gamma-ray state of the quasar starting in 2009 September is simultaneous with an increase of the flux in the mm-wave VLBI core. We resolve a superluminal feature on the VLBA images that appears to be responsible for the mm-wave flux increase. We find a strong correlation between optical and gamma-ray light curves with a delay of gamma-ray variations of 5+/-3 days, as well as a strong correlation between optical flux and degree of polarization during the high gamma-ray state. Comparison between the optical polarization position angle and that in the VLBI core supports the idea that in the quasar 1633+382 a high gamma-ray state is connected with processes originating near the mm-VLBI core.