The accident occurred about 5:30 p.m. on the Roaring Rapids ride at Six Flags over Texas, said Arlington police spokesman Dee Anderson.
Correspondent Betty Nguyen of CBS affiliate KTVT-TV in Dallas reports that the boat was about 200 feet from the end of the ride when it capsized with 12 on board.
Most apparently were able to quickly unbuckle their seat belts and escape the overturned boat, but one woman was unable to unbuckle her belt.
Twenty-eight-year-old Valeria Cartwright, part of a large group visiting the park from West Helena, Arkansas, apparently drowned, Anderson said.
Eleven other people were treated at the hospital, but most of the injuries were believed to be minor.
"I couldn't believe it really happened," said eyewitness Wendy Crown. "One or two people popped up but there was a lot of screaming, a lot of confusion."
In the ride, the round raft-like boats carrying up to 12 passengers each float through a series of rapids in water up to about four feet deep.
Anderson said an initial investigation didn't reveal a possible cause for the accident.
Six Flags spokeswoman Nancy St. Pierre said it was the first customer death at the park in its 38 years.
"It's been a devastating day," she said.