The Rio de Janeiro outfit made the announcement Friday, just two days after their 3-0 loss to Argentina's San Lorenzo in their final group match in Buenos Aires, reported Xinhua.
Botafogo president Mauricio Assumpcao said the club hoped to announce Hungaro's replacement by April 15 at the latest.
"We are looking for a winning coach," Assumpcao said during a press conference.
"We still have time to make our decision because there are 10 days until the beginning of the Brazilian championship."
Hungaro took charge of Botafogo last December after Oswaldo de Oliveira left to join Santos. The 50-year-old led the two-time Brazilian champions to seven wins, six draws and 10 defeats.