The group said it launched a drone attack on a cargo vessel in the area on Monday, the latest in a series of missile and drone strikes on shipping which it says are a response to Israel's assault on the Gaza Strip.
Several major freight companies, including MSC, have begun to sail around Africa, adding costs and delays which are expected to be compounded over the coming weeks, according to industry analysts.
About 15% of world shipping traffic transits via the Suez Canal, the shortest shipping route between Europe and Asia.
Combined, the companies that have diverted vessels control around half of the global container shipping market, ABN Amro analyst Albert Jan Swart told Reuters. "Avoiding the Red Sea will lead to higher cost due to longer travel time," Swart said.
Oil major BP also temporarily paused all transits through the Red Sea, a sign the crisis - which has mostly affected goods freight until now - might broaden to include energy shipments. Crude oil prices rose on those concerns on Monday.
The Houthi attacks were forcing companies to rethink their connections with Israel, with Taiwan's Evergreen Marine saying on Monday it had decided to temporarily stop accepting Israeli cargo.
"For the safety of ships and crew, Evergreen Line has decided to temporarily stop accepting Israeli cargo with immediate effect, and has instructed its container ships to suspend navigation through the Red Sea until further notice," it said in a statement.
The war between Israel and Hamas, which began on October 07, has sent shockwaves through the region and drawn in the United States and its allies on one side and Iran-backed paramilitary groups in the Middle East on the other, threatening to cause a broader conflict.
The shipping attacks have prompted the United States and its allies to discuss a task force that would protect Red Sea routes, a move that US and Israeli arch-foe Tehran has warned would be a mistake.
Rico Luman, an analyst at ING, said the diversions were adding at least a week of sailing time for container liners. Typically, shipping goods from Shanghai to Rotterdam takes around 27 days via the Suez Canal.
"This will at least lead to delays in late December, with knock-on effects in January and probably February as the next round will also be delayed," Luman said.
While freight rates will likely increase on these longer voyages too, carriers at the moment are seeking ways to utilize excess capacity, said Zvi Schreiber, CEO of global freight platform Freightos.
"It is unlikely that rates will spike to levels experienced during the pandemic," said Schreiber, referring to the economic effects of COVID-19 from 2020.
Shipping stocks rose across European exchanges in morning trading on Monday after a jump on Friday on bets the shift away from the Suez Canal could boost rates. A.P. Moller-Maersk rose 3.5% in early trade in Copenhagen, before paring some of those gains.
The Suez Canal is an important source of foreign currency for Egypt. Some 90% of world trade is transported by sea.
The International Chamber of Shipping Association said on Friday that the Houthi assault on shipping lanes, which began last month, was an "extremely serious threat to international trade" and urged naval forces in the area to do all they can to stop the attacks.
