BEIJING— Apple Inc. has another headache in China: this time with its latest watch.

For the first time, the Apple Watch can have an independent cellular connection, allowing people to use it to make voice calls and send and receive text and data even if the watch isn’t wirelessly connected to an iPhone.

But in China, the feature was abruptly cut off for new subscribers, without explanation, after a brief availability with one telecommunications company.

Industry analysts say the suspension likely stemmed from Chinese government security concerns related to tracking users of the device, which uses different technology than standard mobile phones.

China strictly regulates mobile phones, and all three major telecom-service providers are state-owned companies. To get a SIM—subscriber identity module—card to operate the phone, users must register under their real names with a network carrier.