Drug trafficking, rape, murder, apostasy and armed robbery are all punishable by death under Saudi Arabia's strict version of Islamic law.
President Joko Widodo criticised the decision on Wednesday, saying the government has officially protested to Riyadh and demanded better protection of Indonesian workers in the country.
We have called Saudi Arabia's foreign minister and conveyed our protest.
Indonesia, however, placed a moratorium on any Indonesian workers going to Saudi Arabia in 2011, after a female worker was beheaded for killing her employer.
The death penalty was carried out despite the Indonesian Government's efforts to provide "maximum legal assistance" by appealing against Ms Tursilawati's death sentence both in court and in a letter to the Saudi Arabian King, Ms Marsudi said.
"President Jokowi must cancel the agreement between Indonesia and Saudi Arabia on the One Channel System [because the execution is] proof that Saudi Arabia does not fulfill the terms and conditions pertaining to the protection of the rights of migrant domestic workers", Wahyu said in a statement.
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During the meeting, Indonesian Foreign Minister Retno Marsudi emphasised the importance of having a mandatory consular notification before carrying out death penalties.
The majority of Indonesian female migrant workers head to Saudi Arabia, with an estimated one million Indonesian women working in Saudi Arabia in 2014, the vast majority of them employed as domestic workers.
"The kingdom of Saudi Arabia has ignored principles of human rights, including a right for everyone to live", Abidin Fikri, a member of Indonesia's parliament, said.
"I also summoned the Saudi ambassador [Usamah Muhammad Al Syuaiby] in Jakarta to meet me in Bali", she told reporters on Tuesday on the sidelines of the Our Ocean Conference in Bali, according to a distributed recording of her interview.
Accordng to news.com, Migrant Care, an NGO advocating for the rights of Indonesian workers overseas, also condemned the execution.
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. She worked as a nurse for a family in the western city of Ta'if.
Observors say Indonesia is unable to criticize other countries that uphold capital punishment without appearing hypocritical.