NEW YORK—Arab Bank PLC, the largest financial institution in Jordan, was found liable for providing assistance to Hamas in the first U.S. jury verdict against a bank in a civil terrorism-finance case.

The verdict in U.S. District Court in Brooklyn potentially opens the door to more litigation under the Antiterrorism Act of 1990, which gives U.S. victims of international terrorism recourse in federal court. It puts banks on notice that they could face civil liability for doing business with clients regardless of whether the...