"We hope to make books and movies available again to our customers in China as soon as possible," a spokeswoman for Apple, the US technology giant, said in a statement.
The services, launched less than seven months ago in China, were shut down last week on demand from the State Administration of Press, Publication, Radio, Film and Television, the New York Times cited unnamed sources as saying.
Apple did not give a reason for the closedown.
Beijing keeps a tight grip on broadcast, print and online media, while restricting access to foreign websites including Google, Facebook and Twitter with a vast control network dubbed the Great Firewall of China.
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China is a key market for Apple, where its products are widely popular, but it has previously been targeted by state-run media over issues such as service and pricing.
State broadcaster CCTV in 2014 accused the California-based company of threatening national security through the iPhone's ability to track a user's location, a threat Apple quickly denied.
The two Apple services compete directly with Chinese firms, New York Times said, suggesting the latest official scrutiny might be driven by government desire to support domestic companies.
Greater China including Hong Kong and Taiwan is Apple's second-largest market after the America and the company relies on the region to drive growth, according to the firm's report for the first quarter of 2016.