The voluntary redundancy plan it the first since Renault started producing in South Korea in 2000 and is motivated by a 33 per cent slump in sales in the first half of 2012 compared to the same period last year.
The company said 4,500 employees are eligible for the package but that 1,000 research and design staff are not eligible.
It is offering to pay two years’ salary and education costs for children, a lump sum and help in finding a new job, a spokesperson told the Dow Jones news agency.
Application will be closed on 7 September.
Renault sold about 83,000 units in the first six months of 2012 and is expected to build about 180,000 cars during the course of the year. The Busan plant has a 300,000-vehicle capacity.
At the end of July the Renault-Nissan alliance announced the investment of 130 million euros to produce the 4x4 Nissan Rogue at Busan from 2014.
Renault has suffered most of all South Korean carmakers from the effects of global economic slowdown but is not alone in declaring redundancies.
About 130 managers at GM Korea, whose sales fell 2.1 per cent in the January to July period, have applied to go, according to press reports.
There are strong trade unions at Hyundai and Kia, which together rank fifth in global sales, and the company has not recently implemented any major redundancy programme.
South Korea is the fourth biggest economy in Asia.