Read all about this (and Osama is even involved). But wait, it's also in Minnesota. And in New Jersey (Nat'l Group for Communications & Computers Ltd. v. Lucent Technologies Int'l, Inc., 331 F. Supp. 2d 290 (D.N.J. 2004)).
Oddly enough, the American courts treat this as a perfectly normal matter. In the first two cases I cited, the parties entered into a contract that provided for Sharia arbitration; the courts considered challenges to the arbitral process, and upheld the awards. The third case involved a contractual provision expressly stating that disputes about the contract would be resolved under Saudi Arabian law; the court then dutifully investigated what the Saudi rules (which are built on Sharia) would call for, and rendered judgment "based upon this Court's review of various academic texts, the testimony of the experts, the submissions of the parties, and the Court's understanding of the fundamental principles of Islamic law as they would be interpreted by a court in Saudi Arabia."
And of course the application of Sharia law was indeed a perfectly normal matter. American courts are governed by American law, but American law has long provided that parties to contracts can provide for alternative dispute resolution mechanisms (such as arbitration). American law has likewise long provided that some contractual disputes would be resolved with reference to foreign law, especially when the law is expressly provided for by the contract. It doesn't matter whether the arbitration or the foreign law is secular or religious -- secular and religious rules are treated basically equally, on the principle that the parties' contractual choices should be honored unless some extraordinary circumstance makes it unfair to do so.
One could argue that American courts shouldn't be able to apply religious rules because of concerns about excessive entanglement of the government and religion. But even if that's so in some situations, it wouldn't apply when a court is merely asked to confirm an arbitration award rather than to applying the religious rules in the first instance, and it also wouldn't apply when the religious rules are part of the law of a foreign country (such as Saudi Arabia).
Now maybe Sharia law is more likely to be unfair than other systems in certain circumstances; and doubtless some people feel strong social pressure to enter into contracts endorsed by their cultural group. But people feel various kinds of pressure to enter into various kinds of contracts. American law usually enforces the contracts despite talk of pressure and unfairness. There are exceptions, but they are indeed exceptions, and the rule is enforcing contracts. Yet the skies haven't fallen, nor do they seem likely to fall even if more contracts end up being arbitrated or otherwise evaluated under Sharia law.