After a trial, Layla bint Abdul Mutaleb Bassim was executed for killing her husband's daughter Kalthoum bint Abdul Rahman bin Ghulam Gadir, aged six, the ministry said, quoted by the official Saudi Press Agency.
The child died from a beating and being raped with a broomstick, the ministry said.
Authorities identified Bassim, executed in the holy city of Mecca, as holding "Burmese nationality".
Myanmar's embassy in Riyadh said that without seeing her passport, it could not confirm whether or not she was a citizen of that country.
Rape, murder, apostasy, armed robbery and drug trafficking are punishable by death in Saudi Arabia, which executed 87 people last year compared to 78 in 2013, according to an AFP tally.
The execution brings to seven the number of death sentences carried out this year in the conservative Muslim kingdom.
The kingdom had the third-highest number of recorded executions in 2013, behind Iran and Iraq, Amnesty International said in a report.
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