Malaysian and international organisations including the UN's human rights body had this week issued appeals for authorities to stay the expected execution of Gunasegar Pitchaymuthu.
However, Amnesty said two brothers, Ramesh Jayakumar and Sasivarnam Jayakumar, also had been hanged Friday.
AFP was not able to confirm the hangings. Malaysia does not publicly announce executions and otherwise closely guards information on its application of the death penalty.
Malaysian officials have indicated in recent years that the government may review its use of capital punishment, but no progress is known to have been made.
"The fact that these state killings come at a time when the Malaysian government is actively discussing abolition of the mandatory death penalty makes them all the more shocking and disturbing," Amnesty International's Southeast Asia campaigns director Josef Benedict said in a statement.
"These hangings are a sickening reminder that the Malaysian authorities must redouble their efforts to establish a moratorium on executions as a first step towards abolition of the death penalty."
The Southeast Asia office of the UN High Commissioner for Human Rights on Thursday also had urged a stay of Gunasegar Pitchaymuthu's execution, adding that it was "concerned by Malaysia's practice of carrying out executions in secret".
Around 900 people were on death row in Malaysia, officials have said in recent years, mostly drug offenders.
Since 1960, nearly 450 people have been executed, according to data released in 2011, but activists say they have been extremely rare in recent years.
In 2014, authorities halted plans to execute a Malaysian convicted murderer, Chandran Paskaran, after an outcry from rights groups.