The alerts, which also covered the major Red Sea city of Jeddah, nearby Taif and the coastal oil hub of Yanbu, were all rescinded minutes later.
Residents were instructed to "proceed to the nearest safe place" by the agency. The agency also repeated a legal warning against sharing images or information related to "countering missiles and drones".
The Gulf kingdom has come under repeated attack from Yemen's Iran-backed Houthis in recent weeks as part of the latter country's revived civil war.
The group, which is fighting the Saudi-backed internationally recognised government, has targeted the kingdom's oil infrastructure as well as its airports.
An attack on Riyadh airport earlier this month killed 13 people and wounded dozens more.
Riyadh leads a military coalition that first intervened in the conflict, which has devastated Yemen and created one of the world's worst humanitarian crises, in 2015.
The war had been dormant since a ceasefire in 2022, but erupted again in July as the wider Middle East war roiled the region.
