Faris Salam Salama al-Maghrebi was arrested while attempting to "smuggle a large amount of amphetamine" stimulant capsules into the kingdom, the ministry said in a statement carried by SPA state news agency.
He was beheaded in the northern Jawf province, it said.
His execution brings to 16 the number of people beheaded in Saudi Arabia so far this year.
In 2012, the kingdom executed 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.