WASHINGTON—The Justice Department is gearing up for an antitrust investigation of Alphabet Inc.’s Google, a move that could present a major new layer of regulatory scrutiny for the search giant, according to people familiar with the matter.

The department’s antitrust division in recent weeks has been laying the groundwork for the probe, the people said. The Federal Trade Commission, which shares antitrust authority with the department, previously conducted a broad investigation of Google but closed it in 2013 without taking...