Amnesty International said the sentence against Siti Zainab was carried out despite suspicions she was mentally ill.
Her case adds to what the London-based watchdog calls a "macabre spike" in Saudi executions this year.
The interior ministry said Zainab was executed after being convicted of stabbing and beating Saudi woman Noura al-Morobei to death.
Authorities carried out the sentence on Tuesday in the Muslim holy city of Medina, the ministry said in a statement carried by the official Saudi Press Agency.
Zainab's execution brings to 60 the number of foreigners and Saudis executed this year, according to an AFP tally.
Jakarta's embassy in Riyadh declined to comment on the case.
According to Indonesian newspaper Kompas, Zainab was convicted of killing her employer in 1999, despite concerns about her mental health.
Her execution was delayed until the victim's children were old enough to decide whether the punishment should go ahead, the Saudi interior ministry said.
"Imposing the death penalty and executing someone with a suspected mental illness smacks of a basic lack of humanity," said Philip Luther, Amnesty's Middle East and North Africa director.
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A United Nations resolution has called on states not to execute or impose the death penalty on people with mental disorders, Amnesty added.
"She had no legal representation at any stage and did not have access to a consular representative during the police interrogation when she had made her 'confession'," Amnesty said.
It cited sources in Indonesia as saying Zainab admitted to stabbing her employer 18 times because of alleged mistreatment.
Indonesia four years ago announced a moratorium on sending migrant workers to the kingdom, but the Saudi newspaper Arab News reported in January that negotiations between the two countries over the recruitment of domestics had resumed.
Rights groups regularly denounce abuse and even torture of impoverished women from Bangladesh, Indonesia, Sri Lanka, the Philippines and Nepal who work as maids in Gulf countries.
Saudi Arabia in 2013 passed new rules that grant domestic workers one day's rest a week and guarantee the payment of their salaries.
Drug trafficking, rape, murder, apostasy and armed robbery are all punishable by death under the kingdom's strict version of Islamic sharia law.
Saudi Arabia has seen a surge in executions this year, compared with the 87 death sentences carried out in 2014.
Amnesty's 2014 global report on the death penalty ranks Saudi Arabia among the top five executioners in the world.
The Interior Ministry has cited deterrence as a reason for carrying out the punishment and says executing murderers aims "to maintain security and realise justice".