Israel-based Teva had said in July it intended to sue after the Sandoz unit of Novartis applied to U.S. regulators to sell a generic version of the medicine.
The lawsuit, filed in U.S. District Court in Manhattan, claims that any generic version of Copaxone infringes patents that Teva contends are valid and enforceable.
Teva, itself a large maker of generic drugs, has maintained it has patent protection on Copaxone in the United States until May 2014 and in much of Europe until 2015.
Cambridge, Massachusetts-based Momenta said last month that the generic Copaxone application asserts that Teva's patents are invalid.