The warning came after the country's largest oil and gas firm Equinor recently said it had notified authorities of sightings of drones of unknown origin flying near some of its platforms.
"We would urge increased vigilance, a review of emergency preparedness measures and incident response, and information sharing," the PSA said in a letter to operators.
The safety watchdog said unidentified drones posed a risk to helicopters that transport offshore workers, could become an ignition source in areas with explosion hazard, or could be used for deliberate attacks.
Newspaper Stavanger Aftenblad reported last week that unidentified drones had been observed at least at six Equinor installations, including at its giant oilfield Johan Sverdrup.
Last Tuesday, a drone was observed some 50 meters away from Equinor's Heidrun platform in the North Sea, breaching the 500-metre security perimeter, the newspaper reported.
"There have been observations of drones at some of our installations on the Norwegian continental shelf," a spokesperson for Equinor told Reuters, declining to elaborate.
Equinor has reported the incidents to the Norwegian authorities, including the PSA and police.
"We are taking those sightings very seriously," the company spokesperson added.
Drones have been also observed near Kristin, Gullfaks C, Snorre A and Gina Krog installations, Aftenbladet reported.
Norway's southwestern police district said it had started an investigation into sightings of drones offshore and had notified the Norwegian Police Security Service, which deals with terrorism and external threats.
"The police are taking seriously observations of illegal drone activities, and are monitoring the situation closely," lead investigator Amund Preede Revheim told Reuters in an email.
(Reporting by Nerijus Adomaitis; Editing by Jan Harvey)