Japanese shipping operator Nippon Yusen suspended sailings through the Red Sea on Tuesday after the Houthi movement vowed to step up attacks on vessels in the region.
The Houthi group has threatened to expand its targets to include US ships in response to UK and US strikes on its sites in Yemen.
Attacks by the Houthis on ships in area since November have impacted companies and alarmed major powers, in an escalation of Israel's more than three-month war with Hamas militants in Gaza.
As well as disrupting supply chains, there are fears that the attacks could make it more difficult for policymakers to keep global inflation in check.
British and American ships had become "legitimate targets" due to the strikes launched on Yemen last week, Nasruldeen Amer, a spokesperson for the Houthis, told Al Jazeera.
Underlining concerns, Nippon Yusen, also known as NYK Line, has instructed its vessels navigating near the Red Sea to wait in safe waters and is considering route changes, a company spokesperson said on Tuesday.
In the latest apparent attack, the US Central Command said Houthi forces in Yemen struck the US-owned and operated dry bulk ship Gibraltar Eagle with an anti-ship ballistic missile on Monday. There were no reports of injuries or significant damage.
Container vessels have been pausing or diverting from the Red Sea that leads to the Suez Canal, the fastest freight route from Asia to Europe. Many ships have been forced to take the longer route via South Africa's Cape of Good Hope instead.
Also speaking in Davos, Chinese Premier Li Qiang said it was important to keep global supply chains "stable and smooth".
About 12% of world shipping traffic transits the Suez Canal via the Red Sea.
Military strikes will not contain Houthi attacks on commercial shipping but an end to the war in Gaza will, Qatar's prime minister said in Davos.
"We need to address the central issue, which is Gaza, in order to get everything else defused," said Sheikh Mohammed Bin Abdulrahman Al Thani.
Russia pounds Kyiv with missiles, killing at least nine
Trump says deal reached to disarm Hamas, Israeli support for plan remains uncertain
Kuwait intercepts new wave of Iranian attacks
India's Modi says punishing student protesters will not resolve situation
