Vijay Kumar Saleem, of India, was convicted of killing a Yemeni by striking him in the head with the axe, an interior ministry statement carried by the official Saudi Press Agency said.
The attack took place after a dispute at the farm where they worked, it said, adding that Saleem was executed in Riyadh.
Authorities also carried out a death sentence against the Pakistani, Hafiz Wifaq Rasoul Shah, in the Muslim holy city of Medina.
The Pakistani city of Karachi is a key transit point for heroin from Afghanistan.
According to the United Nations Office on Drugs and Crime, the Gulf has become an increasingly important market for illicit drugs in recent years.
The Saudi government says it "is committed to fighting drugs of all kinds due to the physical and social harm they cause".
It also says the death penalty in murder cases aims "to maintain security and realise justice".
Drug trafficking, rape, murder, apostasy and armed robbery are all punishable by death under the Gulf kingdom's strict version of Islamic sharia law.
The London-based watchdog said some defendants claimed to have been tortured or "otherwise coerced or misled into making false confessions" before trial.
According to an AFP count, the kingdom executed 87 people last year, up from 78 in 2013.
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