Mohammed al-Mahameed was caught smuggling a significant amount of amphetamines, the ministry said in a statement carried by the SPA state news agency.
He was beheaded in the northern Jawf region.
Two Saudis convicted of drug trafficking were executed in Eastern Province on the first day of the year.
Saudi Arabia has stepped up its use of the death penalty despite repeated appeals from the United Nations and human rights watchdogs.
The kingdom executed 87 people last year, according to an AFP tally, up from 78 executions recorded in 2013.