The execution was carried out after the death sentence was endorsed by the king, the ministry added in a statement, according to the country's official news agency SPA.
The convict confessed to having knifed to death the six-year-old girl in June 2013, allegedly in retaliation for her family’s ill-treatment.
Monday’s beheading brings to 119 the total number of executions so far this year in the conservative kingdom.
Saudi Arabia is among the top executioners in the world, according to international rights groups.
On January 2, authorities beheaded 47 people, including a prominent Shiite cleric, on terrorism-related charges.
Saudi Arabia imposes the death penalty for murder, armed robbery, banditry, rape, drug-trafficking and witchcraft.
The kingdom, which applies a strict interpretation of Islamic law, has repeatedly rejected calls to end the death penalty, saying the punishment deters would-be offenders.