Can I get my order for protection from Minnesota enforced in another state?
Yes. If you have a valid Minnesota OFP that meets federal standards, it can be enforced in another state. The Violence Against Women Act (VAWA), which is a federal law, states that all valid OFPs granted in the United States receive "full faith and credit" in all state and tribal courts within the US, including US territories.* See How do I know if my OFP is good under federal law? to find out if your OFP qualifies.
Each state must enforce out-of-state OFPs in the same way it enforces its own orders. If the abuser violates an out-of-state OFP, s/he will be punished according to the laws of whatever state you are in when the order is violated. This is what is meant by "full faith and credit."
* See MN Statutes § 518B.01(18)(a)(4)