Singapore’s government said he had been “allowed entry on a private visit”. It is not clear if Mr Rajapaksa will stay or move to another destination.
He pledged to resign by Wednesday amid public anger over the island’s economic crisis, but has failed to do so yet.
The cost of food, fuel and other basic supplies have soared for Sri Lankans.
The president fled to the Maldives on Tuesday night on a military plane and there has been much speculation about his plans.
“He has not asked for asylum and neither has he been granted any asylum. Singapore generally does not grant requests for asylum,” Singapore’s foreign ministry said, confirming he had landed.
The leader, who as president enjoys immunity from prosecution, is believed to have wanted to leave Sri Lanka before stepping down to avoid the possibility of arrest by an incoming administration.
It comes as acting president Ranil Wickremesinghe on Thursday imposed a curfew for a second day. His government ordered a curfew from noon (06:30 GMT) to 05:00 Friday to quell protests.
Mr Wickremesinghe was appointed acting president by President Rajapaksa after the latter fled – but the decision triggered further protests demanding the PM also resign.
One person died and 84 others were injured during Wednesday’s protests, which took place at key landmarks around the capital, Colombo, including the prime minister’s office.
