While not all yokai wear masks, many do, such as the 3 yokai serving as Natori Shuuichi's shiki. Many of the other yokai that meet Natsume also wear masks.
In the story where Natsume was taken by some yokai to be presented to their boss, after he broke out of his confinement, he wore a mask to disguise himself. He also wore a mask for the same purpose when he joined the festival to take a magical kimono that enables the wearer yokai to be seen by humans. Thus it can be concluded that when a human wears a mask, it is to prevent yokai from learning that they are human.
Yet, why do yokai wear masks? What is the mythological background behind yokai wearing masks?