Freight disruptions are emerging in Europe and Asia as the impact of Russia’s invasion of Ukraine ripples across the region, causing delays to the movement of goods and sparking warnings of higher shipping costs.

Freight forwarders including Denmark-based DSV A/S and Germany-based Deutsche Post AG’s DHL express and freight units suspended services to and from Ukraine, closed offices in the country and told workers to focus on their families.

Forwarding executives said most services in and around Russia are still operating but could be sidetracked by last-minute disruptions as diplomatic tensions between Russia and Western nations intensify and as Western-imposed sanctions push companies to examine their shipments more closely.

Airfreight in the region is coming under pressure as aircraft avoid flying close to Ukraine and as diplomatic tensions worsen between Russia and Western nations. Russia on Friday banned airlines flying aircraft registered in the U.K. from operating in its airspace in response to a British ban a day earlier on regular flights from Russia.

French logistics operator Geodis said Friday it expects further airspace closures or airline-specific restrictions that could cause delays, reductions in capacity and rate increases.

Glenn Koepke, general manager of network collaboration at FourKites Inc., a Chicago-based freight-tracking technology supplier, said the war will cause steep shipping rate increases, especially between Asia and Europe, as the conflict disrupts movement of goods by ocean, air and land.

FourKites said cargo volumes that move by rail from China through Russia to the European Union may be shifted to ocean or air if that burgeoning freight connection is disrupted, potentially driving up rates in those transport markets. The company said more than 300,000 containers, measured in 20-foot equivalent units, moved by rail from China to the European Union in the first six months of last year.

U.S.-based Flexport Inc. said Friday it has stopped accepting trans-Siberian rail bookings and is offering air and ocean alternatives instead. Ryan Petersen, Flexport’s chief executive, said the firm is doing so mostly out of concern that customers could lose cargo if service is disrupted.

London-based Drewry Shipping Consultants Ltd. said Friday that although the initial impact on global shipping is small, the geopolitical tensions could add to global economic volatility and send rising fuel costs and inflation still higher.

The conflict is also causing delays to air cargo. Flexport’s two 747 cargo freighters that usually fly over Russian and Ukrainian airspace between Asia and Europe are now taking a longer route over the Middle East, the company said.

“We’re monitoring the situation closely, including the developing sanctions environment imposed by the U.S. and other governments, to see what additional logistical, safety and compliance changes may be required in our operations,” Mr. Petersen said.

Marex Media