We explore the amount of obscured star formation as a function of environment in the Abell 901/902 (A901/902) supercluster at z = 0.165 in conjunction with a field sample drawn from the A901 and CDFS fields, imaged with the Hubble Space Telescope as part of the Space Telescope A901/902 Galaxy Evolution Survey and Galaxy Evolution from Morphology and Spectral Energy Distributions (SEDs) Survey. We combine the combo-17 near-UV/optical SED with Spitzer 24 mu m photometry to estimate both the unobscured and obscured star formation in galaxies with M-* > 10(10) M-circle dot. We find that the star formation activity in massive galaxies is suppressed in dense environments, in agreement with previous studies. Yet, nearly 40% of the star-forming (SF) galaxies have red optical colors at intermediate and high densities. These red systems are not starbursting; they have star formation rates (SFRs) per unit stellar mass similar to or lower than blue SF galaxies. More than half of the red SF galaxies have low infrared-to-ultraviolet (IR-to-UV) luminosity ratios, relatively high Sersicindices, and they are equally abundant at all densities. They might be gradually quenching their star formation, possibly but not necessarily under the influence of gas-removing environmental processes. The other greater than or similar to 40% of the red SF galaxies have high IR-to-UV luminosity ratios, indicative of high dust obscuration. They have relatively high specific SFRs and are more abundant at intermediate densities. Our results indicate that while there is an overall suppression in the SF galaxy fraction with density, the small amount of star formation surviving the cluster environment is to a large extent obscured, suggesting that environmental interactions trigger a phase of obscured star formation, before complete quenching.