It said the recall will affect units of the two models made at the company's Chennai plant between 2004 and 2012.
"Ford India is voluntarily inspecting 39,315 Ford Fiesta Classic and previous-generation Ford Figo vehicles...For a potential concern related to high-pressure power assisted steering hose," it said in a statement.
The company, through its dealers, will replace the high-pressure power assisted steering hose on all affected vehicles, it added.
Ford remains committed to delivering world-class quality vehicles to its customers and this voluntary safety recall is part of that commitment, it said.
Last year, the company had recalled around 42,300 units of the new generation of hatchback Figo and compact sedan Figo Aspire to fix a software glitch that could lead to malfunctioning of airbags during a collision.
In November 2015, the automaker had announced recall of 16,444 units of compact SUV EcoSport in India to fix faulty rear twist beam bolt, a part in vehicle's suspension.
Ford South Africa recalls India-built Figo, Ikon models
Ford South Africa said today it will recall nearly 16,000 Figo and Ikon cars built in India due to a potential fire risk.
The cars, built between August 2004 and March 2012, require Ford technicians to replace the "high-pressure power assisted steering hose, which may split, resulting in a power steering fluid leak", Ford said.
"A power steering fluid leak could result in fumes being emitted from the engine compartment. It may also be possible for power steering fluid to come into contact with the vehicle's exhaust system components, creating the potential for smoke and, in extreme cases, fire," the company said.