Keeping Workers Safe Act This bill requires the Department of Labor to notify the public about certain enforcement actions taken against an employer for safety and health violations. First, Labor must issue a notice of each enforcement action with a penalty greater than $60,000. Second, Labor must issue a notice of each enforcement action resulting from (1) multiple, serious violations, or (2) repeated violations classified as other-than-serious. Labor must issue a notice within seven days of taking the enforcement action and distribute it through regional and local newspapers in the area where the employer is located; applicable trade, industry, or labor organizations; and relevant state and local government entities.