HONG KONG — Japanese automakers suffered plunging sales in China last month and have cut manufacturing by up to half in China this month after violent anti-Japanese protests against Japanese-brand cars and even their owners.

Toyota announced on Tuesday that its sales to dealerships in China dropped 49 percent in September compared with those in the month a year earlier, while Honda said that its sales had fallen 40 percent and Nissan said that sales were down 35 percent.

Mazda said last week that its sales fell 35 percent last month. Industrywide sales data is not yet available for September because not all automakers have reported sales yet. Automakers’ sales to dealerships rose 7 percent for the first eight months of this year compared with those in the period a year earlier. But dealerships have complained of rapidly rising inventories of unsold cars, making it likely that automakers may need to slow shipments to dealerships at some point unless the current economic slowdown in China is suddenly reversed.

Japanese automakers have sharply cut production schedules through the end of October, a sign that they see little immediate improvement on the horizon, although they have followed corporate traditions so far of refraining from layoffs. Automakers release figures only for their sales to dealerships in China because the government has halted the release of retail sales figures by dealerships to consumers for the last year.