Others to be cut included Roma midfielder Marquinho and one-time Arsenal winger Wellington Silva, reports Xinhua news agency.
"We are working to have a group of players that will allow us to be competitive in 2018 while remaining within our budget," the club's executive director Marcus Vinicius said. "We are making a concerted effort to reduce our salary commitments."
Goalkeeper Cavalieri, capped three times for Brazil, represented Fluminense 352 times over seven seasons. Henrique, a centre-back, made seven appearances for the national team after his 2015 move from Napoli.
In addition, the club announced the departures of forward Maranhao, left-back Arthur, midfielder Higor Leite and striker Robert.
The four-time Brazilian top flight champions finished 14th in the country's 20-team Serie A standings in 2017 with just 11 wins from 38 matches.
Fluminense will begin pre-season training on January 3 at their Barra da Tijuca headquarters in Rio's west.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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