A woman called Zhen Zhen told the South China Morning Post that she liked the colour of the cups and how the cat's claws appeared inside when they were filled up.
"I think girls can't resist it," she said.
Her husband bought one for her on Tuesday at a Starbucks store in Zhongshan, Guangdong province.
He was the first customer in the shop when the doors opened at 7am.
"It's so cute! I showed it on WeChat and Douyin and received many likes," Zhen Zhen said.
Douyin is the short-form video app known as TikTok outside China.
A short video of milk being poured into one of the cups was "liked" more than 280,000 times.
One Weibo user said she went a Starbucks outlet in Beijing but found the cups were sold out.
"I love cats. So this cup is really attractive to me," she wrote.
The Cat Claw Cup is one of a cherry blossom-themed series the coffee chain launched during the week across its 3700 outlets on the mainland, Starbucks China said.
"We didn't expect it to be so popular," the company said.
"We guess people have affection for elements such as the colour pink, pet cats and cherry blossoms."
But not everyone was impressed.
"If you put water in it, it doesn't look so beautiful," one Douyin user wrote.
Another said the colour was "too heavy".
"It can't hold much liquid," she wrote. "If you have bought this cup, you will be disappointed."
On Sina Weibo, China's Twitter-like service, Starbucks said it would sell the cups on Tmall.com until the weekend.
The runs were limited to 1000 cups each day and customers could order only one each.
-South China Morning Post
