The 73-year-old fled to the Maldives on July 13 after days of violent protests at home over his mishandling of the island nation's economy.
Immigration authorities in Singapore said that Rajapaksa entered the city-state on July 14 for a private visit. His short-term visa expires on Thursday.
Sri Lankan protesters stormed Rajapaksa’s official residence in early July as the economic crisis worsened, forcing thousands into the streets across the country.
The import-dependent nation ran out of foreign cash reserves in spring and has been suffering from shortages of food, fuel and other essentials. It is up to the new president, Ranil Wickremesinghe, to negotiate a bailout with the International Monetary Fund.