For the second time in a year, Alphabet Inc.’s Google is facing charges from European regulators of abusing a dominant market position to bolster other parts of its business. This time, the allegations strike at the fastest-growing part of its core search unit: mobile phones.

The European Union on Wednesday accused Google of using its Android mobile-operating system, which runs more than 80% of the world’s smartphones, to strong-arm phone makers and telecom companies into favoring Google’s search engine and browser on their...