Mitchell ran the first leg of the men's 4 x 400m Relay and helped the USA finish joint fastest qualifiers for the final as they and the Bahamas were given identical times of 2:58.87.
But the 25-year-old will not contest the final after an X-ray confirmed he had broken his left fibula bone during his run.
Mitchell said: 'Three days ago I was going up the stairs (in the Olympic Village) and I kind of missed one and landed awkwardly. I got treatment and I was fine.
'I did work-outs and when I warmed up today I felt really well. I felt I could go 44 (seconds), low. I got out pretty slow, but I picked it up and when I got to the 100m mark it felt weird. I was thinking I just didn't feel right.
'As soon as I took the first step past the 200m mark I felt it break. I heard it. I even put out a little war cry, but the crowd was so loud you couldn't hear it. I wanted to just lie down. It felt like somebody literally just snapped my leg in half.
'I knew if I finished strong we could still get it (the baton) around. I saw Josh Mance motioning me in for me to hand it off to him, which lifted me. I didn't want to let those three guys down, or the team down, so I just ran on it. It hurt so bad. I'm pretty amazed that I still split 45 seconds on a broken leg.'
USA Track and Field Chief Executive Officer Max Siegel said: 'Manteo has become an inspiration and a hero for his team-mates. Without his courage and determination to finish, Team USA would not be at the starting line in the final.
'The team has rallied around him and we are all looking forward to the final days of competition.'