The plane was over Kansas when it ran into turbulence, but safely landed at Denver International Airport at around 7:45 p.m.
FAA spokesman Ian Gregor in Los Angeles said 26 passengers and four crew members were injured. He said one person was critically hurt, but he released no further details.
Officials said many of the injured were transported to a handful of area hospitals with only moderate injuries. By late Tuesday, some had been released or were expected to be released.
"There are mostly walking injuries," Tade told The Denver Post. He said the injuries included bruises, whiplash, strains and sprains.
The remaining passengers will be taking another United flight to LAX later this evening.
"The plane dropped probably 20, 30 feet," said passenger Alexander Walan. "I saw at least two people hit the ceiling. (Some were) thrown in front of me two rows, hit the ceiling and slammed back down. Luckily I had my seatbelt on.
Flight 967 was carrying 255 passengers and 10 crew members, according to United Airlines spokeswoman Megan McCarthy. She said the crew decided to be safe and land the Boeing 777 in Denver to tend to the injured.
United Airlines has had other rocky flights this year.
In February, about 20 people were injured when a United flight experienced turbulence halfway through a 13-hour trip from Washington, D.C., to Tokyo. The Boeing 747 had 263 people onboard.
In May, 10 people suffered injuries, including broken bones, on a United flight that hit severe turbulence over the Atlantic Ocean on its way from London to Los Angeles. The Boeing 777 was diverted to Montreal.
The Associated Press contributed to this report.