The two-week-old strike by 220 000 Numsa union members, who are seeking 12-15% annual increases, follows on the heels of a five-month strike in the platinum sector that stunted economic growth and export earnings.
The manufacturing strike has also forced General Motors to close its assembly plant in the southern city of Port Elizabeth over a week ago, despite efforts by Labour Minister Mildred Oliphant to mediate between the union and employees.
"Production at our Silverton assembly plant has been temporarily suspended due to the strike," Ford spokesperson Alicia Chetty said on Monday, adding that only the company's Pretoria plant was affected and its other plant in Port Elizabeth was operating normally.
Toyota said it will halt some production from Tuesday because of supply chain problems related to the stoppage.
"Toyota will close two production lines from Tuesday at our Durban plant," spokesperson Mary Willemse said.
German car maker Mercedes Benz said on Monday supplies to its South African plant were "critical" due to the strike, although production was still continuing.
"Supply lines are becoming critical due to the National Union of Metalworkers of South Africa (NUMSA) strike in the engineering and metals sector," the head of Mercedes' local unit, Arno van der Merwe, said in a statement.
Production at BMW, VW and Nissan was normal, although company officials said on Monday they were monitoring the situation closely.
Other companies affected are construction companies Murray & Roberts and Aveng, which are working on the construction of two major power plants for state power utility Eskom.
Numsa rejected the latest pay offer from employers in the steel and engineering sector on Sunday and called on its striking members to intensify the industrial action.
Employers have offered pay rises of 10% in the first year, 9.5% in the second year and 9% in the third year. But unions also have grievances about the role of labour brokers in industry and do not want to be bound to a multi-year agreement, preferring a one-year deal instead.
The union and employers were due to meet on Monday for further talks.
Smaller union United Association of South Africa (UASA), which represents about 20 000 workers in the sector, said it was awaiting a response from employers on questions about the same offer.
"We expect an answer by tomorrow and that will put us in a position to say if we accept or reject it but chances of accepting look good," said Johan van Niekerk, UASA spokesperson.
The strike, which has hit the supply of beverage cans made by packaging firm Nampak has damaged wider investor sentiment in Africa's most advanced economy, which is teetering on the brink of recession after a first-quarter contraction caused in part by the platinum strike.
Ratings agency Standard & Poor's cut South Africa's credit rating last month while Fitch put it on negative watch, both citing poor growth prospects mainly because of strikes.
The Reserve Bank's monetary policy committee meets on Thursday to consider an interest rate hike amid growth concerns after the central bank raised it by 50 basis points to 5.50% in January, the first increase in almost six years.
"If growth is the main concern, governor (Gill) Marcus may be unwilling to raise the repo rate unless the strike is resolved soon," Francois Stofberg, an economist at Efficient Group said.
Analysts have long singled out South Africa's volatile labour environment as a deterrent to investment.
Separately, about 200 workers downed tools at unlisted Cape Town-based wine maker DGB, demanding a 10% wage hike, union leaders said. DGB, which makes some well-known brands, is offering a 7% raise.