Google Inc.’s planned wireless service may launch by the end of March, but it will work only on the company’s latest Nexus brand smartphone and not on other phones using Google’s Android operating system, people familiar with the matter said.

The service, designed to switch among Wi-Fi and cellular networks, will initially be available only on the latest Nexus 6 smartphone designed by Google and made by Motorola Mobility, a former Google unit now owned by China’s Lenovo Group Ltd., two people familiar with the matter said....