I'm with @roamer_1 on this: I think it will be the County to step in, with their own county laws and procedures. They will necessarily have to staff up dramatically, and Minneapolis has a lot of cops who will be looking for a job. The County may just send a bill to the City or State.
County won't be interested in stupid ordinances to enforce, they'll go with the work they're tasked with...busting Felonies and Misdemeanors, then jailing the perps. The City won't be able to order Sheriff's Deputies around, the way they do with the City cops. This is a bad move from the city's point of view.
That is the structure that is already in place. It is not a military zone, subject to international peacekeepers (which is where they want to take it no doubt).
The peacekeeping forces in this country are interleaved, depending upon sworn officers, beholden to the Constitution and the constitution of their state. Those forces interoperate within jurisdictions... The city within the county's jurisdiction, and the county within the state's.
if ALL of that breaks down, even to the point of the state's martial authority being overcome, the next step is still not international. At that point it becomes the interest of the federal government to restore order...
Just because a city decides to put its papers of corporation at risk, does not mean there is no law.
And the mayor of Minneapolis knows it. He's done bit off more than he can chew... And now gets to weight the loss of revenue and power against the quelling of riots that he helped to incite.
And the county authority remains in place. as does the state's.