Briefing Parliament's portfolio committee on agriculture, forestry and fishers, Fawu general secretary Katishi Masemola said the EU was selling breast portions to their member countries at premium prices and "dumping" leg quarters in South Africa at "ridiculously low prices".
This, he said, had already led to a few thousand jobs being shed in the local industry.
"The situation is going to get even more dire if nothing is done so tens of thousands of these jobs are at stake," Masemola told African News Agency (ANA) on the sidelines of the meeting with MPs.
"By June it wouldn't be far-fetched to talk about close to between five and seven thousand jobs which are likely to come to an end."
South Africa's biggest poultry company, Astral Foods, had reduced hours for workers and closed some shifts, reducing the weekly pay of its employees instead of complete retrenchment, Fawu told MPs.
At Rainbow chicken, the second biggest poultry company in the country, 1,350 jobs were lost due to the firm closing some of its farms in KwaZulu-Natal and down-scaling of its processing operation.
Masemola also informed MPs the third biggest company, Country Bird Holdings, had announced the closure of three of its abattoirs, meaning several hundred workers are likely to be laid off.
He said workers were feeling trepidation, hoping government would do something to help save their jobs.
"They are all worried and these are unskilled workers who have no further hope of employment so there's a sense of anxiety."
While the effect of the EU chicken imports have not yet effected the entire value chain, Fawu believes jobs would soon be at stake at feed companies.
"In the maize industry there's likely to be down-scaling, so we just saying there may be a lag, but the knock-on effect is likely to be following," said Masemola.
"Feed companies attached, vertically integrated to your main chicken producers they will also downscale because they don't have to source more maize to process chicken feed."
Masemola said a "trade war" with the EU may be "inevitable".
"We may not have a choice but to implement technical barriers for chicken coming from Europe in the same way they are doing for our chicken going into their shores," he said.
"They've got an avian flu right now. We can stop chicken coming from Europe and then we can also place other technical barriers to trade such as safety standards, such as health standards, which they demand of us."
Government recently established a poultry sector task team to deal with the crisis in the domestic poultry industry.
The Task Team is comprised of representatives of the dti, the departments of economic development, agriculture, forestry and fisheries, the Industrial Development Corporation, Poultry South Africa, and Fawu.