The interior ministry said Amal Jan Hajji had been found guilty of killing Bambang Sukyato and his wife Suryati Widyastuti.
He broke into their home and beat them with a metal object, it said, without giving a motive for the killing.
Indonesian embassy officials could not be immediately reached.
Authorities carried out the sentence against Hajji in Riyadh.
Pakistani Beheaded: Heroin trafficker executed in Saudi
According to AFP tallies, he is the 139th foreigner or Saudi executed in the kingdom this year, compared with 87 in 2014.
Most Saudi executions are carried out by beheading with a sword, in what the ministry says is a deterrent.
Rights experts have raised concerns about the fairness of trials in the kingdom.
Saudi Arabia may run out of financial assets in 5 years, warns IMF
London-based Amnesty International says Saudi Arabia had the world's third-highest number of executions last year, far behind China and Iran, and ahead of Iraq and the United States.
Under the kingdom's strict Islamic legal code, murder, drug trafficking, armed robbery, rape and apostasy are all punishable by death.
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