Apple Inc. is manufacturing its new Mac Pro computer in China, according to people familiar with its plans, shifting abroad production of what had been its only major device assembled in the U.S. as trade tensions escalate between the Trump administration and Beijing.

The tech giant has tapped Taiwanese contractor Quanta Computer Inc. to manufacture the $6,000 desktop computer and is ramping up production at a factory near Shanghai, the people said. Apple can save on shipping costs for components given the proximity of many...