Optical reflectivity experiments have been conducted on single crystals of the Kondo insulator YbB12 in order to obtain its optical conductivity, σ(ω). Upon cooling below 70 K, a strong suppression of σ(ω) is seen in the far-infrared region, indicating the opening of an energy gap of ∼25 meV. This gap development is coincident with a rapid decrease in the magnetic susceptibility, which shows that the gap opening has significant influence on magnetic properties. A narrow, asymmetric peak is observed at ∼40 meV in σ(ω), which is attributed to optical transitions between the Yb 4f-derived states across the gap. In addition, a broad peak is observed at ∼0.25 eV. This peak is attributed to transitions between Yb 4f-derived states and the p-d band, and is reminiscent of similar peaks previously observed for rare-earth hexaborides.