The explosions that killed dozens in Tianjin disrupted operations at one of the world’s busiest ports, a complex of shipping berths and warehouses that serves as northern China’s gateway for factory exports and imported consumer goods.

Logistics operators and cargo handlers on Thursday were still trying to determine the extent of the damage to the large volumes of container shipments, automobiles and commodities near the blast zone. One container terminal operator part-owned by Danish conglomerate A.P. Moller-Maersk A/S said it was rapidly returning to normal operations after shutting down after the explosions.

However, a logistics company with a large presence at Tianjin said in an email to employees that some container yards had been “heavily damaged” and that communications at some warehouses and storage sites were destroyed. The operator said customs authorities had moved to a temporary location and were operating “at very low efficiency.”

“We can foresee that all ocean freight cargo will be delayed dramatically in the coming weeks,” the company told its workers.

Tianjin and its port are at the center of one of China’s economic zones—regions with special laws and ownership restrictions to facilitate international trade. The port is part of a sprawling free trade zone the government opened in Tianjin in April to tie industrial activity in northern China more closely to the port and spur more trade and foreign investment.

Along with numerous Chinese-owned manufacturing facilities, major Western corporations, including Airbus Group SE, Deere & Co. and Wal-Mart Stores Inc. operate factories or distribution centers in the area. Factories across the region rely on Tianjin to export their goods and to import iron ore, coal, oil and other commodities. The port is also one of the top importers of cars in China.

Ken Golden, a spokesman for Deere, said in an emailed statement that the industrial equipment manufacturer has suspended its Tianjin operations while it assesses damage to its facility, which is eight miles from the explosion site, and assists employees. He said several Deere workers “who were home at the time of the blasts have sustained serious injuries and some are in critical condition.”

British drug giant GlaxoSmithKline PLC said one of its manufacturing sites had been affected by the blast but a spokesman said it was too early to say to what extent. GSK’s operations in Tianjin are focused on the manufacture of consumer health products.

Tianjin ranks 10th globally in container traffic, handling about 14 million twenty-foot-equivalent units, the standard measure for containers, according to Alphaliner, a research firm. That’s about the same number as the combined volume at Los Angeles and Long Beach, the largest U.S. port complex, though it lags the busiest southern Chinese ports, including Shanghai and Shenzhen.

Tianjin “is absolutely an enormous port … it’s of huge importance in respect to the distribution of goods around the northern region of China, especially the Beijing metropolitan area,” said John Manners-Bell, chief executive of U.K.-based logistics research firm Transport Intelligence Ltd.

He said even minor delays could ripple across supply chains because major ports like Tianjin serve as focal points for global shipping as well as transportation inland. He added that it’s too early to know how the explosions will affect logistics for companies that use the port.

“This is a huge, huge risk … ports are transport nodes within the supply chain,” Mr. Manners-Bell said.

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The explosions could have an immediate effect on the price of iron ore imported by steelmakers, according to Nicolai Hansteen, an analyst with shipbroking firm Lorentzen & Stemoco AS in Oslo.

The port has been expanding its iron ore import capabilities in recent years to accommodate the largest ore ships. In 2008, China Cosco Holdings Ltd., a state-owned shipping line, established a new headquarters for its dry bulk shipping operations in Tianjin. The port imported 25 million tons of iron ore in the first half of 2015, or roughly 6% of China’s projected total imports this year, according to data analyzed by Lorentzen.

Government data also show that Chinese steel mills have drawn down stocks of iron ore to roughly 80 million tons, or about 20 days’ supplies, Mr. Hansteen said.

“It’s fallen to a very precarious levels. Any disruption in that respect will be felt as a shortage, and it will be felt as high prices.”

APM Terminals, the Maersk-owned operator, said it had resumed outbound shipping, with inbound traffic expected to restart on Friday. APM handled nearly 1.8 million containers last year at Tianjin, or just over 10% of the total at the port, and manages loading and unloading for ships operated under an alliance between Maersk and Mediterranean Shipping Co., the two biggest container shipping lines.

Tom Boyd, an APM spokesman, described the area nearest to the explosions as a staging ground for industrial exports.

“This is the processing area before things get into the port, with a lot of consolidation and a lot of storage,” he said, adding that the timing of the blasts, coming late Wednesday, probably limited casualties.

“If it had happened during the business day, during working hours, this would have been considerably worse,” Mr. Boyd said.

Overseas Orient Container Line, a unit of Hong Kong-based Orient Overseas (International) Ltd. notified customers by mail that “no doubt that there will be disruptions” to shipping to and from the area. The carrier said cargo on four vessels, three of them operated in an alliance with the Hyundai shipping line, may be affected by the blast but that it was still collecting information on specific shipments.

—Robbie Whelan and James R. Hagerty contributed to this article.