Ramalho, who won the Brazilian championship four times in five years after a hat-trick of titles with Sao Paulo, cited the poor infrastructure at the Rio de Janiero club and a lack of response despite repeated requests for improvements.
"When I arrived at the club (in April 2010) I was promised two things: a team to become champions and an improvement in the physical structure of the club," Ramalho said in a statement.
"We achieved the first with the title in the 2010 Brazilian championship and the second, an improvement in the structure, was not realised," he added after Fluminense drew 0-0 with Flamengo in a Carioca (Rio) state championship derby.
"I would very much like to thank everyone who worked with me during this period and say my cycle at this club is closed," added Ramalho, whose resignation came a day after Fluminense sacked the club's director of football Alcides Antunes.
Ramalho's departure could exacerbate Fluminense's problems this season, especially in the Libertadores Cup which they began among the favourites but are in danger of a group phase exit after picking up only two points in three matches.
"We'll work to the death so Fluminense need never again go through this. You have a team that are Brazilian champions, a first notch coach and you see that trainer leave because he feels he doesn't have adequate working conditions," club president Pieter Siemsen told reporters at the Engenhao stadium.
Ramalho's decision came as a shock given his reputation for not breaking his contracts.
Chosen by the Brazilian Football Confederation (CBF) to replace 2010 World Cup coach Dunga after Brazil's quarter-final defeat by the Netherlands in South Africa, Ramalho did not accept the job because Fluminense would not release him from his contract.
Sao Paulo's 18-year-old playmaker Lucas celebrated his first Brazil call-up in midweek with a brilliant performance including a goal in his club's 3-0 win over Santo Andre in the Paulista (Sao Paulo) state championship.
Lucas, included in coach Mano Menezes's squad for Brazil's friendly against Scotland in London on March 27, scored with a fantastic volley into the top right corner from outside the box to put Sao Paulo two up on the hour.
Striker Dagoberto had opened the scoring at the Morumbi and Casemiro headed their third after a shot from Lucas came back off the bar.
"You can't be afraid to take risks. If I'd tried to control of the ball, the defender could have robbed me and started a counter-attack. Thank God it was a good shot and I managed to score that great goal," Lucas told reporters.
Another talented young Brazil midfielder who has already been capped by Menezes, 21-year-old Paulo Henrique Ganso returned from a seven-month injury layoff to help Santos beat Botafogo-RP 2-1 on Saturday.
Playing as a second-half substitute, Ganso laid on the opener for Brazil midfielder Elano and scored the second.
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