The infrared (IR) activities of vibrational modes in molecular solid hydrogen at megabar pressures have been studied by performing a first-principles calculation of the polarizations using the geometric phase approach. We have studied the Cmc21 and the Pca21 structures as candidate structures for phase III (H-A or D-A). In the Cmc21 case, the high-frequency vibron gives higher IR intensity than the low-frequency vibron, which agrees with the experimental results although the effective charge of the high-frequency vibron is much larger than the experimental value. In the Pca21 case, the high-frequency vibrons give lower IR intensities than the low-frequency vibron, which contradicts the experimental findings. Also, in the Pca21 case, two IR phonons are possible although one IR phonon is observed in phase III.