The interior ministry said a Saudi citizen, Rabie al-Sai'ari, had been convicted of trying to smuggle hashish into the kingdom.
He was executed in Najran, a district on the border with Yemen, a ministry statement carried by the official Saudi Press Agency said.
The ministry has cited deterrence as a reason for its use of the death penalty despite criticism from human rights watchdogs.
Amnesty International ranked Saudi Arabia among the world's top three executioners of 2014.
On a visit to Riyadh this month, French President Francois Hollande said that 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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