Stellar multiplicity properties have been studied for the lowest and the highest stellar masses, but intermediate-mass stars from F-type to late A-type have received relatively little attention. Here, we report on a Gemini/NICI snapshot imaging survey of 138 such stars in the young Scorpius-Centaurus (Sco-Cen) region, for the purpose of studying multiplicity with sensitivity down to planetary masses at wide separations. In addition to two brown dwarfs and a companion straddling the hydrogen-burning limit which we reported previously, here we present 26 new stellar companions and determine a multiplicity fraction within 0 ''.1-5 ''.0 of 21% +/- 4%. Depending on the adopted semimajor axis distribution, our results imply a total multiplicity in the range of similar to 60%-80%, which further supports the known trend of a smooth continuous increase in the multiplicity fraction as a function of primary stellar mass. A surprising feature in the sample is a distinct lack of nearly equal-mass binaries, for which we discuss possible reasons. The survey yielded no additional companions below or near the deuterium-burning limit, implying that their frequency at >200 AU separations is not quite as high as might be inferred from previous detections of such objects within the Sco-Cen region.