Workers at Kia, which is 39% owned by Hyundai, voted in favour of two stoppages during Monday's working time.
Staff at Hyundai walked off the job for a third day on Monday, and more stoppages are planned for this week.
Workers are demanding better pay and improved conditions, as well as assurances about job security and future redundancies.
Almost three-quarters of Kia's 27,000 union members voted in favour of the strike.
"We don't see a major impact", a spokesman said.
Kia said the planned stoppages would cut output by 10,569 vehicles, costing more than £54m. Union officials said they were seeking an 8% increase in basic pay, shorter working hours and more say for staff in managerial decisions. Management spokesmen say unions actually are seeking a 12% pay hike.
Hyundai has said it cannot accept workers' demands because record oil prices had pushed up its costs at a time when foreign sales have been falling.