Orion is Nasa's next-generation astronaut vehicle, which will take humans to Mars and other destinations.
The American aerospace giant Lockheed Martin is developing the front section, which includes the crew capsule.
The structural test article, despatched by Airbus, will be used to check the overall design is on track.
It is the first time the US has gone outside its territory for a key component of an astronaut transportation system.
Engineers are working towards an unmanned demonstration flight in 2018, and a first crewed outing no later than April 2023.
The European Space Agency's contribution - being primed industrially by Airbus - is what is called the "service module".
This is the element that pushes Orion through space after coming off the top of the launch rocket.
It also provides the electrical power, and holds the air and water needed by the crew in their protective capsule.
The structural test article is an exact replica of the eventual module - but without the final functionality.
It has gone from Airbus's subcontractor on the project, Thales Alenia Apace in Italy, to Nasa's Plum Brook Station in Ohio where it will be evaluated.
The module's mass and interfaces with the American element will need to be checked.
The article will also be loaded and stressed to ensure it can handle the intense vibrations of launch.
Any lessons learned will then be fed back into the fully functional flight hardware being made ready for 2018.
That mission will see the debut of Nasa's new "monster rocket" - the Space Launch System.
It will send the complete Orion system on a trip around the Moon.
The capsule itself has already had one demonstration trip into space - in December 2014, again with no-one onboard.
On that occasion, the service module was a dummy used just to replicate the size and shape of the real element.
Europe's design for the future service module borrows heavily from the unmanned cargo truck it used to re-supply the space station.
At one time, Europe thought of adapting this vessel into a human transportation system of its own, but baulked at the costs.
Jonathan.Amos-INTERNET@bbc.co.uk and follow me on Twitter: @BBCAmos
The test model for what will become the European-built "back end" of America's Orion spaceship has been despatched to the US.