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.1 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."
1 See MN Statutes § 518B.01(18)(a)(4)