Baz Mohammed Ghul Mohammed was found guilty of attempting to smuggle a "large amount of heroin" by hiding it in his stomach, the ministry said in a statement carried by SPA state news agency.
He was executed in the Eastern Province city of Khobar, the ministry said.
The Gulf state last year beheaded 78 people, according to an AFP count.
A United Nations independent expert in September called for an immediate moratorium on the death penalty in Saudi Arabia.
Christof Heyns, the UN special rapporteur on extrajudicial, summary or arbitrary executions, has said Saudi trials "are by all accounts grossly unfair" and defendants 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.
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