Mohammad Yunus Mohammed Shoaib, executed in the Eastern Province community of Qatif, "was caught smuggling a large quantity of heroin into the kingdom inside his gut," the ministry said in a statement carried by the official Saudi Press Agency.
His decapitation takes to 57 the number of people executed by sword in the ultra-conservative Gulf nation this year, compared with 78 people in all of 2013, according to an AFP count.
On Tuesday a Saudi, Hamad bin Awadh bin Hawi Al-Anzi, was executed in northern Jawf region "because he smuggled a large quantity of amphetamine pills into the kingdom," SPA said.
A United Nations independent expert in September called for an immediate moratorium on the death penalty in Saudi Arabia.
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Christof Heyns, the UN special rapporteur on extrajudicial, summary or arbitrary executions, said trials "are by all accounts grossly unfair" and defendants are often not allowed a lawyer.
He said confessions were obtained under torture.
Rape, murder, apostasy, armed robbery and drug trafficking are all punishable by death under Saudi Arabia's strict version of Islamic sharia law.