Staff called to a meeting yesterday for the announcement were ''devastated'', the Meat Workers Union said.
The proposal was due to a significant decline in processing numbers over the last 10 years and the opportunity to process the consolidated volume at SFF's Pareora site, south of Timaru, chief executive Dean Hamilton said.
Before 2010, Fairton consistently processed more than a million lambs each season but last season it put through less than half a million.
The slide continued this year, when just over 325,000 animals were processed in a six-month seasonal operation.
While the company believed the pace of land-use change had slowed considerably, it expected sheep numbers to consolidate around current levels, rather than expand in the foreseeable future.
''It makes economic sense to consolidate this volume at our nearby Pareora site, which has the capacity to process the combined numbers,'' Mr Hamilton said.
SFF recently spent $7 million at Pareora on a new venison plant and a cold storage upgrade.
A small amount might have to be spent to cope with the additional capacity but it would not be significant, he said.
The decision was not about SFF ''getting smaller in sheepmeat'' in the South Island. It was quite the opposite - the company wanted to retain and grow volumes.
The decline in sheep numbers because of the change in land use was physically obvious to ''everyone that drives around'' and also those working in the plant. Because of that, there had been a high expectation something had to change, he said.
A two-week consultation period was proposed, although if there was significant feedback that was too short or too long, then that would be considered. It was hoped to have a final decision on May 31.
Support was being offered to the 370 affected staff. If the decision was made to close, the company would help them with opportunities at other sites, he said.
It was expected there would be 230 jobs available at SFF plants in Belfast and Pareora, as well as at Hokitika, and further jobs at sites around the country as the new season commenced.
It was intended to retain operation of the pelthouse at Fairton, which further processed all the company's pelts in the South Island. It employed 23 staff.
As long as the pelthouse was operating, SFF needed the around 400ha of land it owned. It was not farmed, but used for distributing water.
In October last year, SFF confirmed the closure of its Mossburn venison processing plant in Northern Southland, affecting 43 jobs, and Frasertown mutton processing plant at Wairoa, affecting 67 positions. Those workers were given options to transfer to other plants.
Asked if any other plant closures could be expected soon, Mr Hamilton said Fairton was a significant closure and the company wanted to focus on that and do it right.
The company would be watching where lamb numbers headed but he confirmed no more closures were intended this year.
Meat Workers Union national secretary Graham Cooke said while the union would take part in the consultation process, it did not have high hopes of a change in decision by the company.
It was tragic for the meat workers and the Ashburton community, he said.