Bighead and silver carp from Asia have been detected in those waterways after migrating north in the Mississippi and Illinois rivers for decades.
Officials poisoned a section of the Chicago Sanitary and Ship Canal this month to prevent the carp from getting closer to Lake Michigan while an electrical barrier was taken down for maintenance.
But scientists say DNA found north of the barrier suggest at least some of the carp have gotten through and may be within 6 miles of Lake Michigan. If so, the only other obstacle between them and the lake are shipping locks and gates, which open frequently to grant passage for cargo vessels.
The lawsuit asks for the locks and waterways to be closed immediately as a stopgap measure, echoing a call by 50 members of Congress and environmental groups last week. But the suit goes further, also requesting a permanent separation between the carp-infested waters and the lakes.
That would mean cutting off a link between the Mississippi and Great Lakes basins created more than 100 years ago, when Chicago reversed the flow of the Chicago River and began sending sewage-fouled Lake Michigan water south toward the Mississippi River.
"The Great Lakes are an irreplaceable resource," Cox, who is seeking the Republican gubernatorial nomination in Michigan, said at a news conference in Detroit. "Thousands of jobs are at stake and we will not get a second chance once the carp enter Lake Michigan."
He likened the notorious fish to "nuclear bombs." The biggest Asian carp can reach 4 feet in length and weigh 100 pounds while consuming up to 40 percent of their body weight daily in plankton, the base of the Great Lakes food chain.
Cox went directly to the Supreme Court because it handles disputes between states.
Michigan is seeking to reopen a case dating back to 1900, when Missouri filed suit against Chicago over its re-engineering of the river.
After that issue was resolved, several Great Lakes states -- including Michigan -- renewed the suit with a new complaint: Chicago's diversion of water away from the basin was harming the lakes by lowering water levels.
The high court has ruled on the matter numerous times, setting ceilings on the amount of Lake Michigan water Chicago could divert. The present limit is 2.1 billion gallons per day.
Michigan's suit argues that continued operation of the locks represents another potential injury to the lakes. It asks the court to immediately order them closed, and to create new barriers to prevent the carp from entering the ship canal from nearby waterways during floods.
Obama administration officials last week pledged $13 million to prevent carp from bypassing the electronic barrier by migrating between the Des Plaines River and the canal.
The lawsuit also asks the Supreme Court to require a study of the Chicago waterway system to define where and how many carp are in those waters and to eradicate them.
Noah Hall, an assistant professor at Wayne State University's law school, said Michigan has a good chance of prevailing if it can show the potential harm posed by Asian carp would outweigh the benefits of keeping the locks open.
"The carp invasion is a good textbook example of irreparable harm," Hall said.
Illinois Attorney General Lisa Madigan's office was reviewing the suit and had no immediate comment, spokeswoman Natalie Bauer said.
Metropolitan Water Reclamation District spokeswoman Jill Horist said, "It's unfortunate that there would be an assumption that this would make some positive resolution come sooner than is truly feasible. Even if the locks were closed there's still a variety of ways for DNA or Asian carp to enter Lake Michigan."
Spokeswoman Lynne Whelan said the Army Corps could not comment on pending litigation.
Democratic Gov. Jennifer Granholm and Rep. Candice Miller, a Michigan Republican, praised the lawsuit.
"There is nothing more pressing than stopping this aggressive invasive species from entering Lake Michigan and threatening our lake's environment and all the states' economies in the Great Lakes Basin," Miller said.
Environmentalists said closing the locks would be a temporary fix, but the only long-term solution would be restoring the natural separation between the Great Lakes and the Mississippi River system, which Michigan is now seeking.
"The Chicago diversion was a 19th century solution to an environmental problem. Now it's causing a 21st century emergency," said Andy Buchsbaum, director of the National Wildlife Federation's Great Lakes center.
American Waterway Operators, a trade group of U.S. barges and tugs that haul cargo on the waterways, said closing the locks even temporarily "would be very devastating for our industry ... but also for people in the Chicago region."
It would force vessels to offload their cargo onto trucks or rail cars, boosting transportation costs and air pollution, vice president Lynn Muench said.
Michigan's lawsuit said losses to barge traffic and recreational boats would be "relatively minor and finite." In contrast, it said, "If the Asian carp enter the Great Lakes system, the damage to the environment and economies of the Great Lakes states and Canadian provinces will be staggering with no practical end in sight."