There is, on November 19th. Its stated goals are to bring more awareness to issues men face, like suicide, abuse, homelessness, and violence. It also is for celebrating men’s lives, achievements, and contributions.
The joke (if you do need it explained) is Women’s Day without fail brings sexist men out of the woodwork. They bitterly complain about it, and whine that having such a day set aside just for women is discrimination, and that there should be a Men’s Day (totally either not realizing or not caring that such a day exists already).