Khadija bint Mohammed Isa was executed in Hafar al-Batin, northeast Saudi Arabia, it said in a statement carried by the official Saudi Press Agency (SPA).
She had "killed three-year-old child Aljazi bint Mohammed bin Fahd al Harbi... by stabbing her 30 times while she slept in her parents' room," the ministry said.
The suspect fled but was later captured and convicted, it said.
Local media said Isa was a maid, although SPA did not clarify her employment status or say what led to the killing.
Working conditions of more than 2.4 million foreign maids in Saudi Arabia and other Gulf countries have been widely criticised.
Saudi Arabia last year passed new rules that grant maids one day of rest a week and guarantee the payment of their salaries.
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Isa was the latest of 78 foreigners and Saudis -- most of them men -- executed in the kingdom this year despite international concerns over the number and judicial process.
The kingdom "is keen to protect security and justice", the interior ministry said.
Authorities also executed a convicted Saudi drug dealer on Tuesday, it said.
Nasser bin Amiq Ali al-Inzi was found guilty of trying to smuggle "a large amount" of amphetamines into the country.
He was beheaded in the northern Jawf region.
The interior ministry said last week that authorities had seized more than 41 million amphetamine tablets during the Islamic calendar year that ended in October.
Rape, apostasy and armed robbery are also punishable by death under the kingdom's strict version of Islamic sharia law.