This would be an increase of 39.9 per cent over the level of 2013-15, during which there were 2.7 million tons, on average.
According to FAO, fishing grows at a much lower rate and the total fish production in the region would reach 16.2 million tons in 2025. This figure would be 12.6 per cent higher than the level 2013-15, from 14.4 million tons.
The report said regional exports of fishery products are growing faster than imports.
"Although we are far from the production generated in Asia, Latin America and the Caribbean has begun to establish itself as an exporter of fishery and aquaculture products for direct and indirect human consumption, maintaining one of the highest rates of aquaculture expansion in the world," said Alejandro Flores Nava, Head of Fisheries and Aquaculture for the FAO's Latin America and Caribbean Regional Office.
Mr Flores stressed that an important task for the region is to stimulate local consumption of seafood, especially in schools.
The full report, entitled 'The State of World Fisheries and Aquaculture (SOFIA) 2016' is available here.