It then changed direction suddenly, hurting more people standing on the other side.
The float's driver is being questioned.
The vehicle, belonging to the Paraiso de Tuiuti samba school, "went into reverse and ended up pressing revellers against the fence on one side," police investigator William Lourenco Bezerra said.
"The main driver of the float mixed with the rest of the samba school and left. But he has already been identified and will be investigated," Mr Bezerra added.
Jaime Cezario of Porto da Pedra samba school told Brazil's Folha newspaper that the float "veered left towards the stands".
"People had nowhere to flee," he said. "Then it went right at high speed, where I was. We had to throw ourselves to one side so we wouldn't be crushed," he said.
The school was the first of six to take part in the parade on Sunday and organisers decided to continue with the event.
"It is all regrettable, but we cannot stop,'' organiser Elmo dos Santos said.
About 70,000 people were in the Sambadrome watching the parade, but only those at the entrance, where the accident occurred, were aware of what happened.
The annual carnival ends on Wednesday.
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