As a precaution, responders also checked on a 27-year-old female flight attendant, who was also serving passengers and fell to the floor, Chapman said. The medical team prescribed over-the-counter pain medication.
Chapman said the captain had the seat belt sign on, and no passengers were injured.
Cathy Burden of Edmonton, Alberta, was among the mostly families and couples traveling from Edmonton to the Mexican resort town for vacation. She said the turbulence was "pretty scary."
"The flight attendant was just bringing a tray of champagne, and she went up in the air and the champagne went everywhere," she told The Associated Press. "Nobody actually got a glass, but we all got champagne on us."
She said she saw the flight attendant fall to the ground, but didn't see anyone on board with serious injuries. She said everyone was "a bit rattled."
After landing in Helena, the state's capital, passengers waited for hours on the tarmac because a customs agent couldn't immediately get to the airport.
Helena Regional Airport Director Ron Mercer said the airport has one agent who wasn't available Sunday, so another one made the 90-minute drive from Great Falls.
He said the airport doesn't typically deal with international commercial flights, so the customs agent had to make sure international rules were followed before the passengers could get off the plane.
They exited into a secure area of the terminal, where the passengers had access to food and restrooms but couldn't leave the area. Chapman said allowing them to wander the terminal would have caused problems when it came to resuming their journey because they're international travelers.
Nonetheless, she said, the passengers had been "reported to be in very good spirits."
Another aircraft was sent from the company's headquarters in Toronto to pick up the passengers so the initial plane could be examined for damage, Chapman said, a move she called customary after severe turbulence is encountered.
The aircraft hit the rough patch northwest of Helena, somewhere over the Continental Divide, Mercer said.
The second jet and a new crew arrived in Helena on Sunday evening, and the passengers took off for Mexico.
"This winter that will not end," Chapman said. "They're attempting to escape it. Hopefully, we'll get them there soon."
AP Radio reporter Ed Donahue in Washington contributed to this report.