SHANGHAI—The Trump administration’s latest tariffs will hammer Chinese auto-parts makers, likely raising prices for their U.S. customers, who have few options to buy key parts elsewhere, manufacturers and industry experts say.

The new tariffs on $200 billion of Chinese-made goods, announced Monday and set to take effect next week, are expected to hit a range of auto-related imports—from crankshafts and spark plugs to windshield-wiper blades—and reverberate through the supply chain, potentially impacting the prices of new and...