According to eyewitnesses gunfire can be heard in the vicinity of the palace late on Saturday night.
King Salman was not present in his palace in Riyadh on Saturday when security forces shot down the drone in the area, a senior Saudi official told Reuters.
The statement followed unconfirmed videos on social media that appeared to show heavy volleys of gunfire in that neighbourhood, triggering speculation of a possible coup attempt.
Government officials did not immediately respond to requests for comment on the whereabouts of the Saudi king and crown prince during the incident.
Forget flying ants, exploding ants are here to ruin your summer
A new species of ant has been discovered, which has the ability to explode when under attack in an attempt to save its own colony. Their bodies are full of glandular sacs containing a deadly fluid, said Laciny, a PhD student at the University of Vienna.
Prince Mohammed returned earlier this month from a foreign tour that included the United States where he sought investments and support to curb Iranian influence in the region.
The attacker, who was identified by the interior ministry as Mansour al-Amri, a 28-year-old Saudi national, was armed with a Kalashnikov rifle and three Molotov cocktails.
The young prince has also led his country's war against a Yemeni Zaidi Shiite Muslim rebel group known as Ansar Allah, or the Houthis, which took over the Yemeni capital of Sanaa in 2015.
Saudi Arabia, in the midst of a far-reaching liberalisation drive, will allow women to drive from June and recently permitted them to enter sports stadiums for the first time.