We report the detection of seven low-mass companions to intermediate-mass stars (SpT B/A/F; M similar to 1.5-4.5M(circle dot)) in the Scorpius-Centaurus (Sco-Cen) Association using nonredundant aperture masking interferometry. Our newly detected objects have contrasts Delta L' approximate to 4-6, corresponding to masses as low as similar to 20 M-Jup and mass ratios of q approximate to 0.01-0.08, depending on the assumed age of the target stars. With projected separations rho approximate to 10-30 AU, our aperture masking detections sample an orbital region previously unprobed by conventional adaptive optics imaging of intermediate-mass Sco-Cen stars covering much larger orbital radii (similar to 30-3000 AU). At such orbital separations, these objects resemble higher-mass versions of the directly imaged planetary mass companions to the 10-30 Myr, intermediate-mass stars HR 8799, beta Pictoris, and HD 95086. These newly discovered companions span the brown dwarf desert, and their masses and orbital radii provide a new constraint on models of the formation of low-mass stellar and substellar companions to intermediate-mass stars.