The Saudi, Mohammed al-Qahtani, shot dead fellow national Mueed al-Qahtani in a fight, the ministry said in a statement carried by state news agency SPA.
He was beheaded in the southwestern Aseer region.
In a separate case, Nabil Abu Khanjar, a Syrian, was beheaded in the northern Al-Jawf province after he was convicted of smuggling "large amounts of amphetamines," SPA reported.
Tuesday’s executions bring to 12 the number of people beheaded in Saudi Arabia so far this year.
In 2012, the ultra-conservative Muslim kingdom beheaded 76 people, according to an AFP tally based on official figures. The US-based Human Rights Watch put the number at 69.
Rape, murder, apostasy, armed robbery and drug trafficking are all punishable by death under Saudi Arabia’s strict version of sharia, or Islamic law.
