Apple Inc. acknowledged problems with cellular connectivity in its newest smartwatch, raising questions about the device’s most significant feature days before it goes on sale in stores in the U.S. and other countries.

In a statement Wednesday, Apple said the problem connecting to cellular networks occurs when the Apple Watch Series 3—the first watch from Apple to feature an LTE chip for cellular service—joins “unauthenticated Wi-Fi wireless networks without connectivity.” Apple said it is “investigating a fix for a future...