The Norwegian Maritime Authority (NMA) has raised the security level for its ships following the attack on tankers at Fujairah in the UAE.
At least four vessels were targeted in what appeared to be a mine attack on Sunday, including two from Saudi Arabia and Norwegian manager Thome's 47,000-dwt Andrea Victory (built 2005).
No one has yet admitted responsibility.
"The security level has been increased because we do not know exactly what has happened," NMA said.
"Thus, we see it appropriate to raise the awareness for Norwegian ships in the area. The security level may be adjusted again as soon as we know more about these incidents."
Information about the exact geographical boundaries will be distributed to relevant ships.
NMA had earlier warned vessels in the area to exercise "great caution" and take necessary precautions concerning traffic outside the port.
"The Norwegian Maritime Authority is working with various operators in order to obtain a full overview of all Norwegian registered vessels travelling in this area," it added.
Tensions rose further on Tuesday as Saudi Arabia said armed drones attacked two oil pumping stations in the country.
The government called it a "cowardly" act by Yemen's Houthi rebels.
The strikes caused minor damage to one of the stations supplying a pipeline running from its oil-rich east to Yanbu on the Red Sea, Saudi energy minister Khalid al-Falih said in a statement carried by the state-run Saudi Press Agency.
"These attacks prove again that it is important for us to face terrorist entities, including the Houthi militias in Yemen that are backed by Iran," he added.
