According to estimates, the compensation, which will cover nearly 900,000 vehicles, may cost the firms millions of dollars.
There are also fears that the firms’ sales in the US, one of their biggest markets, may be hurt in the near term.
Both firms’ shares fell 7% in Seoul.
Hyundai Motors was trading at 200,000 South Korean won while Kia Motors was down to 56,300 won early on Monday.
“We believe this could be a game-changing event in Hyundai’s success story,” James Yoon, an analyst at BNP Paribas was quoted as saying in a report by the Reuters news agency.
“We now find improvements in brand perception at risk due to faulty mileage claims, which are at the core of the brand’s success during difficult times.
“We think the potential financial loss is immaterial compared to the potential reputational loss of brand equity.”
The errors were discovered by the US Environmental Protection Agency (EPA).
The agency said the firms had misstated claims on 13 models between them, including Hyundai’s Elantra and Kia’s Rio and Soul.
However, the carmakers blamed “procedural errors at testing facilities in Korea” for the faulty mileage claims.
The firms said they would issue debit cards to the owners of these vehicles to reimburse them for the higher-than-expected fuel costs, based on the difference between their actual mileages and the firms’ claimed mileages.