Iftikhar Ahmed Mohammed Anayat was found guilty of attempting to traffic heroin into the kingdom in balloons concealed in his stomach, the ministry said in a statement carried by the official Saudi Press Agency.
He was executed in the Red Sea city of Jeddah.
The ministry has cited deterrence as a reason for its use of the death penalty despite criticism from human rights watchdogs.
London-based Amnesty International ranked Saudi Arabia among the world's top three executioners of 2014.
READ:Saudi Arabia beheads 80th person this year
On a visit to Riyadh this month, French President Francois Hollande said capital punishment "should be banned", and his country is campaigning around the world for its abolition.
Drug trafficking, rape, murder, apostasy and armed robbery are all punishable by death under Saudi Arabia's strict version of Islamic sharia law.
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