The Empire Builder train derailed at 4 p.m. near Joplin, a town of about 200, Amtrak spokesman Jason Abrams said in a statement. The accident scene is about 150 miles (241 kilometers) north of Helena and about 30 miles (48 kilometers) from the border with Canada.
The train had about 147 passengers and 13 crew members onboard, Abrams said.
Amtrak was working with the local authorities to transport injured passengers and safely evacuate all other passengers, Abrams added.
Megan Vandervest, a passenger on the train who was going to visit a friend in Seattle, told The New York Times that she was awakened by the derailment.
"My first thought was that we were derailing because, to be honest, I have anxiety and I had heard stories about trains derailing," said Vandervest, who is from Minneapolis. "My second thought was that's crazy. We wouldn't be derailing. Like, that doesn't happen."
She told the Times that the car behind hers was tilted over, the one behind that was entirely tipped over, and the three cars behind that "had completely fallen off the tracks and were detached from the train."
Speaking from the Liberty County Senior Center, where passengers were being taken, Vandervest said it felt like "extreme turbulence on a plane."
Photos posted to social media showed several cars on their sides. Passengers were standing alongside the tracks, some carrying luggage.
The images showed sunny skies, and it appeared the accident occurred along a straight section of tracks.