Yes – employers can require assignment of employee inventions under Minnesota law, but there are important statutory limitations on that right that employers need to know.  Minnesota law provides that any assignment in the ownership rights of employee inventions may not apply to:

[A]n invention for which no equipment, supplies, facility or trade secret information of the employer was used and which was developed entirely on the employee’s own time, and (1) which does not relate (a) directly to the business of the employer or (b) to the employer’s actual or demonstrably anticipated research or development, or (2) which does not result from any work performed by the employee for the employer.

Minn. Stat. § 181.78.  The statute further provides that any agreement for assignment of invention rights that purports to apply to inventions that meet the criteria listed above is “void and unenforceable.”
In addition, if an employment agreement contains a provision requiring the employee to assign or offer to assign any of the employee’s rights in any invention to an employer, the employer must, at the time the agreement is made, provide a written notification to the employee that the agreement does not apply to inventions that meet the criteria listed above.
Takeaways:  Employers who require assignment of employee inventions should:  (1) make sure that their agreements relating to the assignment of inventions comply with the statutory exclusions created by Minnesota law: and (2) make sure to provide the written notification required by the statute for employees who are subject to assignment agreements.