Erika said in a series of now-deleted Tweets: "Thanks United, for a terrifying flight! Drunk or stoned stewardess endangered everybody's lives.
"I had to go to the cockpit and call the pilot and tell him they had an out of control attendant. The cops and an ambulance were waiting for her when we landed."
She also posted images of the flight attendant on the social media site.
United responded to Erika's Tweets asking for more details and later apologised to the customers on-board, saying it is refunding all of their airfares "as a gesture of goodwill".
The crew member, who has not been identified, was not arrested upon landing but has been removed from service while an investigation is underway.
Trans States Airlines, which operated the United flight, said in a statement that it is "aware of reports of erratic behaviour by a flight attendant on flight 4689 from Denver to Willston.
"The situation is under investigation and the flight attendant is being held out of service. The safety of our passengers and crew is our and United's top priority."
Meanwhile, there was an outpouring of support on social media for the flight attendant, with concerned Twitter users defending her against allegations she was drunk or drugged.