Federal prosecutors are pursuing a criminal investigation of China’s Huawei Technologies Co. for allegedly stealing trade secrets from U.S. business partners, including technology used by T-Mobile US Inc. to test smartphones, according to people familiar with the matter.

The investigation grew in part out of civil lawsuits against Huawei, including one in which a Seattle jury found Huawei liable for misappropriating robotic technology from T-Mobile’s Bellevue, Wash., lab, the people familiar with the matter said. The probe...