Suzaku and Chandra X-ray observations detected a new cluster of galaxies, Suzaku J1759-3450, at a redshift z=0.13. It is located behind the Milky Way, and the high Galactic dust extinction renders it nearly invisible at optical wavelengths. We attempt here to confirm the galaxy cluster with near-infrared imaging observations, and to characterize its central member galaxies. Images from the VVV survey were used to detect candidate member galaxies of Suzaku J1759-3450 within the central region of the cluster, up to 350 kpc from the X-ray peak emission. Color-magnitude and color-color diagrams and morphology criteria allowed us to select the galaxies among the numerous foreground sources. Fifteen candidate cluster members were found very close to a modeled red-sequence at the redshift of the cluster. Five members are extremely bright, and one is possibly a cD galaxy. The asymmetry in the spatial distribution of the galaxies respect to the X-ray peak emission is an indicator of that this cluster is still suffering a virialization process. Our investigation of Suzaku J1759-3450 demonstrates the potential of the VVV Survey to study the hidden population of galaxies in the Zone of Avoidance.