Abrar Hussein Nizar Hussein was executed in the Red Sea city of Jeddah after being convicted of trying to smuggle in heroin hidden in his stomach, the ministry said in a statement carried by SPA state news agency.
Zahid Khan Barakat was beheaded in Qatif, in Eastern Province, over a similar charge, a separate statement said.
Last year, Saudi Arabia executed 78 people, according to an AFP count.
In 2012, Saudi Arabia carried out 76 executions, according to a tally based on official figures. Rights group Amnesty International put 2012's figure at 79.