The component, called the taptic engine, produces the sensation of being tapped on the wrist, the newspaper reported.
Apple declined to comment on the story.
Apple has not given any sales figures for its hotly anticipated Apple Watch since it began taking orders this month. Chief Executive Tim Cook said on Monday that demand continued to outstrip supply.
Some taptic engines supplied by Shenzhen, China-based AAC Technologies Holdings Inc started to break down over time, the Journal said, citing the people. The company is one of two suppliers of these components to Apple, it said.
As a result, Apple is now sourcing nearly all of its components from the other supplier, Japan's Nidec Corp. It may take time for the company to increase production, the people told the Journal.
The Journal said an AAC spokeswoman declined to comment about the company's customers. Reuters was unable to reach the company for comment outside of regular business hours in China.
Nidec was not immediately available for comment.
© Thomson Reuters 2015
For the latest tech news and reviews, follow Gadgets 360 on X, Facebook, WhatsApp, Threads and Google News. For the latest videos on gadgets and tech, subscribe to our YouTube channel. If you want to know everything about top influencers, follow our in-house Who'sThat360 on Instagram and YouTube.