Paiva's team went out at the last 16 stage with a 1-0 loss after extra-time to fellow-Brazilian club Palmeiras, and the manager has paid the price after just four months in charge.
Botafogo grabbed the spotlight at the Club World Cup when they beat PSG 1-0 in the group stage, having earlier defeated Seattle Sounders, and they advanced as Group B runners-up despite a 1-0 defeat by Atletico Madrid.
"The Club thanks Paiva and his assistants for their services to Botafogo over the last few months," a club statement on social media said.
"Particularly for the historic victory against Paris Saint-Germain in the Club World Cup and the qualification for the round of 16 of the (Copa) Libertadores and Copa do Brasil."
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