Huawei Technologies Co., whose products have been targeted as a national security risk by the U.S. and other governments, faces a new hurdle: reduced access to the global financial system.

Two banks that helped power the Chinese company’s rise as a global technology supplier, HSBC Holdings PLC and Standard Chartered PLC, won’t provide it with any new banking services or funding after deciding that Huawei is too high risk, people familiar with those decisions said.

While...