Mohammed bin Khamees al-Hantushi al-Enzi was found guilty of killing Ibrahim bin Marfu al-Enzi, the ministry said in a statement carried by the SPA state news agency.
His execution in the northeastern city of Hafr al-Batin brings to 12 the number of death sentences carried out this year in the ultra-conservative kingdom.
Saudi Arabia beheaded 78 people in 2013, according to an AFP count.
Last year, the UN High Commission for Human Rights denounced a "sharp increase in the use of capital punishment" since 2011 in Saudi Arabia.
In 2012, the number of executions dipped slightly to 79, among them 27 foreigners.
Rape, murder, apostasy, armed robbery and drug trafficking are all punishable by death under Saudi Arabia's strict version of Islamic sharia law.