Nagaenthran Dharmalingam, 34, had been on death row for more than a decade after he was convicted of trafficking about 43 grams of heroin into Singapore.Â
The city-state's government has said its use of the death penalty for drug crimes is made clear at the borders.
Nagenthran's family and social activists confirmed the execution on Wednesday.
"On this score may I declare that Malaysia is far more humane," his sister Sarmila Dharmalingam said. "Zero to Singapore on this."
Nagaenthran's supporters and lawyers said he had an IQ of 69 and was intellectually disabled, and that the execution of a mentally ill person was prohibited under international human rights law.
"Nagaenthran Dharmalingam's name will go down in history as the victim of a tragic miscarriage of justice," said Maya Foa, director of non-government organisation Reprieve.
"Hanging an intellectually disabled, mentally unwell man because he was coerced into carrying less than three tablespoons of diamorphine is unjustifiable and a flagrant violation of international laws that Singapore has chosen to sign up to."
Nagaenthran and his mother had filed a motion on Monday arguing it was unconstitutional to proceed with his death sentence and he may not have been given a fair trial because the chief justice who presided over his appeals had been the attorney-general when Nagaenthran was convicted in 2010.
The court dismissed the motion, describing it as "frivolous".
His family said Nagenthran's body will be brought to their hometown in Malaysia, where they have made preparations for his funeral.