Prince Turki bin Saud al-Kabir was put to death in the capital. No details were given as to how he was executed - most condemned people are beheaded.
The prince is the 134th person to be put to death this year, according to a list compiled by the AFP news agency.
But it is rare for royal family members to be executed, correspondents say.
The prince had pleaded guilty to shooting his compatriot, the interior ministry statement said.
Announcing the execution, the ministry said it would assure everyone the government was "keen to preserve security and achieve justice".
The victim's family refused offers of "blood money" by which they would receive financial compensation in return for not demanding the death sentence, Al-Arabiya reported.
One of the most well-known cases of a Saudi royal being executed was that of Faisal bin Musaid al Saud, who assassinated his uncle, King Faisal, in 1975.
Most people executed in Saudi Arabia are convicted for murder and drug trafficking although nearly 50 people were put to death for "terrorism" on a single day in January including the prominent Shia cleric Sheikh Nimr al-Nimr.