Mahdi al-Ghabari battered his wife Shaqraa al-Bahri several times on her neck with an axe, killing her "in the presence of their little daughter who witnessed" the crime, said the statement published by the official SPA news agency.
He was executed due to the "hideousness" of the crime, said the statement.
The beheading in the southwestern city of Najran raised to 23 the number of executions so far this year in the Gulf state, according to an AFP count based on official reports.
In 2013, there were 78 executions.
Rape, murder, apostasy, armed robbery and drug trafficking are all punishable by death under Saudi Arabia's strict version of Islamic sharia law.