The 22-year-old, one of the sensations of the pandemic-delayed 2021 Tokyo Games, crashed to the track at around the 200m mark in the final at Hayward Field.
Mu, who was also a member of the USA's victorious 4x400m relay team in Tokyo, crossed the finish line in tears after failing to make up ground following her tumble.
The agonising race highlighted the unforgiving nature of the US Olympic track and field trials, one of the most competitive meetings in world athletics outside of a major championship.
Only the top three finishers of each event qualify for the Olympic squad, which does not take into account other races or performances throughout the season.
Mu, the 2022 world champion, had not raced all season before the trials as she worked her way back from injury.
However she had looked comfortable in the early rounds of the 800m, and had seemed poised to book her place on the Olympic team.
Instead, the US 800m trio in Paris will be headed by Nia Akins, who won in 1min 57.36sec, with Allie Wilson second and Juliette Whittaker third.
In other events on Monday, Quincy Hall won the men's 400m in a time of 44.17sec, pipping Michael Norman, who was second in 44.41sec.
Chris Bailey was third in 44.42 sec, while 16-year-old schoolboy Quincy Wilson missed out on an automatic berth in Paris after finishing in sixth place.
Wilson may still earn an Olympic ticket as part of the 4x400m relay squad.
Meanwhile, world 110m hurdles champion Grant Holloway signalled he is ready to add Olympic gold to his resume after scorching to a world-leading 12.92sec in his first heat.
