Updated from 9:28 a.m. to include analyst comments in the fifth paragraph.
First tweeted by CNBC's Carl Quintanilla, Cook wrote that there is "strong growth for our business in China through July and August," noting that iPhone activations have accelerated over the past few weeks.
Investors have become concerned about Apple's results in China, where the company derives a significant portion of its business.
On the company's fiscal third-quarter earnings call, CEO Timothy D. Cook said the stock market selloff could "create some speed bumps in the near term," but added that the impact will be limited because relatively few Chinese own stocks. "Nothing that's happened has changed our fundamental view that China will be Apple's largest market at some point in the future," Cook said.
Cantor Fitzgerald analyst Brian White noted that the negative sentiment pertaining to China is overblown, at these levels. "Despite the near-term economic malaise in China with the recent devaluation of the RMB that is driving markets lower around the world, we believe the 4G expansion in China, the rise of the middle class and Apple's expansion across the country will continue to provide big opportunities for growth at Apple," White wrote in a note on Monday. He has a buy rating and a $195 price target on shares.