Currently, the country occupies twelfth place internationally and produces 480,000 tonnes of fish in the aquaculture sector.
The MPA's goal is to reach two million tonnes by 2020.
The projections were detailed by the Minister for Fisheries, Helder Barbalho, during a public hearing in the Senate.
The minister said that in the world, the fishing business is seven times greater than that of beef and nine times larger than chicken.
But in Brazil, fish represents only 0.1 per cent of total animal protein exports.
"Seafood is a new frontier of business in which the largest exporter of beef and chicken in the world needs to act," he said.
To quickly achieve this goal, one of the first missions of the Ministry is to improve production in hydroelectric reservoirs, but environmental licensing is an obstacle.
The goals will not be easy to meet in practice, Mr Barbalho said. Increasing aquaculture production faces bureaucratic difficulties with licensing and environmental planning and land tenure.
In addition, producers need a reduction of the cost of inputs such as feed, and they want to obtain similar tax incentives to those granted to other production chains.
The minister also said the government will give priority to improving the lives of workers, by raising the level of education and professional training, and improving health, safety and working conditions.