Indonesian advocacy group Migrant Care said in September that Ms Tuti Tursilawati had been defending herself from being raped.
The office of the cabinet secretary cited the Migrant Care assertion.
The Saudi ambassador to Indonesia had been summoned to discuss the matter, the president said.
"The kingdom of Saudi Arabia has ignored principles of human rights, including a right for everyone to live," said Abidin Fikri, a member of Indonesia's parliament.
Ms Tursilawati was executed just a week after al-Jubeir, met his Indonesian counterpart, Retno Marsudi, and Mr Widodo in Jakarta to discuss migrant workers' rights.
During the meeting, Mr Marsudi emphasised the importance of having a mandatory consular notification before carrying out death penalties.
Indonesia's Government has also called for a thorough probe into the death of Jamal Khashoggi, a Washington Post columnist and a critic of Saudi Arabia's de facto ruler, Crown Prince Mohammed bin Salman.
Saudi Arabia is the world's biggest destination for Indonesian maids and earlier this month the two countries signed a new agreement to jointly "supervise, monitor, and evaluate" the workers.
After the execution, the executive director at Indonesia's Migrant Care advocacy group, Wahyu Susilo, called on Indonesia's government to cancel the agreement.
"It turned out that Indonesia's request [to protect the rights of migrant workers] was ignored by executing Tuti."
Mr Susilo condemned the execution and urged the President to take 'serious' diplomatic steps to prevent future uninformed executions.
There are currently 18 Indonesian migrant workers on death row in Saudi Arabia.
An Indonesian migrant worker, Muhammad Zaini Misrin, was executed in March this year for killing his employer, and two Indonesian female domestic workers, Siti Zaenab and Karni, were beheaded in April 2015.