Prince Turki bin Saud al-Kabir pleaded guilty to shooting Adel al-Mohaimeed following the fight in the capital Riyadh.
Most people executed in the kingdom are beheaded with a sword, though it was not revealed how the prince was killed.
It is rare that members of Saudi Arabia’s ruling family are executed.
The most prominent case was Faisal bin Musaid al Saud, who assassinated his uncle, King Faisal, in 1975.
A ministry statement said: “The government is keen to keep order, stabilise security and bring about justice through implementing the rules prescribed by Allah.
“King Salman’s keenness on enforcement of security, justice and God”s judgments.”
It also warned “that legitimate punishment would be the fate of whoever tries to assault innocent people and shed their blood”.
The victim’s family refused offers of “blood money” in which they would have received compensation for not demanding the death sentence, according to local media.
The majority of people executed in Saudi Arabia are convicted for murder and drug trafficking.
But almost 50 people were put to death for “terrorism” on a single day in January, including the prominent Shia cleric Sheikh Nimr al-Nimr.
Sheikh Nimr was a vocal supporter of the mass anti-government protests that erupted in Eastern Province in 2011, where a Shia majority have long complained of marginalisation.
This sparked a backlash from Shia-led Iran who said the country would pay a “high price” for the execution of Nimr.