Yes, Minnesota law allows public or private employers to “establish policies that restrict the carry or possession of firearms by its employees while acting in the course and scope of employment.”  Minn. Stat. § 624.714, Subd. 18.  This is true even for employees who have lawful “conceal and carry” permits.  However, an employer may not prohibit employees from carrying or possessing firearms in a “parking facility or parking area.”
Employers may also prohibit non-employees from bringing firearms into a Minnesota workplace by prominently posting a sign that reads “[COMPANY] BANS GUNS IN THESE PREMISES.”  The lettering for the sign must be in black arial typeface at least 1.5 inches in height against a bright contrasting background that is at least 187 square inches in area.  See Minn. Stat. § 624.714, Subd. 17.
Takeaways:  Employers in Minnesota who are concerned about employees or non-employees potentially bringing guns into the workplace should adopt policies and post signs warning that guns are banned on the premises.  Employers should take caution, however, that the ban against firearms does not extend to any parking areas or parking facilities.