The Malaysian, who was working in a petrol station, was arrested at the Woodlands checkpoint for possession of 22.24g of heroin, which were found in a black bundle in the centre armrest console of the auto he was driving.
The 29-year-old who is from Johor Baru, was hanged to death at the Changi Prison in the wee hours of the morning.
His lawyers had previously filed for an application with the Appellate Court in Putrajaya for the case to brought up to the International Court of Justice.
Srivijayan's lawyer, Choo Zheng Xi, had asked the Singapore apex court on Thursday to put a stay on his execution on the grounds that his appeal in Malaysia was still pending.
Prabagaran Srivijayan was convicted of drug trafficking and given a mandatory death sentence in 2012 after 22.24g of diamorphine was found in the arm rest of a auto he borrowed.
Throughout the trial, Prabagaran maintained his innocence, insisting he was not aware of the drug being in the vehicle.
Prabagaran, who had said he was unaware that the two bundles were in his vehicle, claimed trial on a charge of importing heroin of more than 15g, which carries the death penalty. However, Prabagaran's petition for mercy was unsuccessful. Court documents said Prabagaran had borrowed the auto from a friend to enter Singapore on that day because he could not use his motorcycle.
He told FMT the appeals court had ruled that Singapore is a sovereign nation and that it would not wait for the outcome of proceedings in Malaysia.
"The judiciary of each country is entitled to act in accordance with its Constitution and its laws", The Channel News Asia quoted Judge Chao as saying.
Amnesty International had expressed concerns about the fairness of the trial.
"Drug-related offences do not fall under the threshold of "most serious crimes".
At present, 103 countries have abolished the death penalty for all crimes and 141 are abolitionist in law or practice. In 2016, four people were executed - two for murder and two for drug trafficking - while at least 38 people were known to be on death row at the end of that year.