Ships will have to obtain a permit from Yemen's Houthi-controlled Maritime Affairs Authority before entering Yemeni waters, Houthi Telecommunications Minister Misfer Al-Numair said on Monday.
Houthi militants have repeatedly launched drones and missiles against international commercial shipping in the Gulf of Aden since mid-November, saying they are acting in solidarity with Palestinians against Israel's offensive in Gaza.
The near-daily attacks have forced firms into long and costly diversions around southern Africa and stoked fears that the Israel-Hamas war could destabilize the wider Middle East. The United States and Britain have bombed Houthi targets in response.
The territorial waters affected by the Yemeni order extend halfway out into the 20-km (12-mile) wide Bab al-Mandab Strait, the narrow mouth of the Red Sea through which around 15% of the world's shipping traffic passes on its way to or from the Suez Canal.
"(We) are ready to assist requests for permits and identify ships with the Yemeni Navy, and we confirm this is out of concern for their safety," Al Masirah TV, the main television news outlet run by Yemen's Iran-aligned Houthi movement, reported Al-Numair as saying.
Damage caused by Houthi attacks
Hong Kong-based HGC Global Communications said on Monday that at least four underwater communications cables - Asia-Africa-Europe 1, the Europe India Gateway, Seacom and TGN-Gulf - had been damaged last week in the Red Sea, without stating the cause.
It estimated that the damage had affected 25% of the data traffic flowing under the Red Sea, and said in a statement that it had devised a plan to reroute traffic.
Al-Numair's ministry on Saturday blamed US and British attacks for any damage to cables.
In the latest incident, the UK Maritime Trade Operations agency said on Monday it had received a report that a vessel had been damaged by two explosions, 91 nautical miles southeast of Aden, but there were no casualties and the vessel was proceeding to its next port of call.