The two men, aged 41 and 50, were arrested shortly after they picked up the ransom money from a suburban park and released the 79-year-old victim, a police statement said.

They did not identify her but the Straits Times newspaper reported that she is the mother of Lim Hock Chee, founder and chief executive of the Sheng Siong supermarket chain which is listed on the main board of the Singapore Exchange.

In a video posted on the newspaper's website, Lim said his mother was lured outside her home into a car by the kidnappers after they told her he had been seriously injured in a fall.

She was held for about 12 hours.

The supermarket chain has more than 30 outlets across Singapore and registered total revenue of Sg$637.3 million ($501 million) in the year to December 2012.

Lim was listed in Forbes' Singapore's 50 Richest List in 2013, with a net worth of Sg$515 million.

Police said the original ransom demand was for Sg$20 million.

"Kidnapping for ransom is very rare in Singapore but is a very severe offence which is punishable by life imprisonment or the death penalty," deputy commissioner of police Hoong Wee Teck said in the statement.

Singapore, a regional financial centre and one of Asia's richest and safest cities, takes a tough stand against crime.

The death penalty -- carried out by hanging -- is mandatory for certain crimes such as murder and can also be imposed for other serious offences such as kidnapping and drug trafficking.