Molinari, once viewed as a rising star in the Republican Party, will be the vice president for public policy for North and South America, Google said in a statement on Thursday.
She replaces Alan Davidson, who began Google's lobbying operation several years ago. He stepped down in November.
Google has faced down one regulatory challenge after another in recent years, but has come through generally unscathed. It won antitrust permission to buy Motorola Mobility and ticketing software company ITA, among many recent acquisitions.
But it has also had setbacks, including a New York court's rejection of a digital books project, a failed bid for a joint venture with Yahoo! Inc in 2008 and a consent decree with the Federal Trade Commission last year following Google's botched rollout of its now defunct social network Buzz. The decree calls for monitoring that lasts 20 years.
Google could also be hurt by efforts to give consumers more privacy online. The White House asked Congress on Thursday to pass a "privacy bill of rights" that would give consumers much more control over the data being collected about them by Internet and other companies.
The FTC, which also investigates violations of antitrust law, is currently looking into complaints that Google's search results favor the company's other services, among other issues.
Google hired 12 lobbying firms this past summer in the wake of the FTC probe, after previously hiring six other lobbying firms.
Government filings show Google has lobbied on issues as disparate as copyright, taxes, cybersecurity, privacy and patent reform.
Molinari, a Republican, was first elected to the House of Representatives in 1990, but stepped down in 1997. She worked in television for a period and then became a lobbyist.
The appointment was first reported by Politico.
(Reporting By Diane Bartz; editing by Andre Grenon)