The BBC reported that a senior State Department official said none of the tomatoes, water bottles and shoes struck Clinton or her vehicle.
The Italian news agency Agenzia Giornalistica Italia reported the "Monica" chant was an apparent reference to Monica Lewinsky, the White House intern alleged to have had an affair with Clinton's husband, then-President Bill Clinton.
AGI said the protest appeared to have been triggered by suspicions that Washington helped Muslim Brotherhood candidate Mohamed Morsi become president of Egypt.
The secretary of state, who was in Alexandria to reopen the U.S. consulate that had been closed since 1993, said the "United States is not in the business, in Egypt, of choosing winners and losers, even if we could, which, of course, we cannot."
"Democracy is not just about reflecting the will of the majority. It is also about protecting the rights of the minority," she said.
Alexandria was her last stop before leaving Egypt.
Earlier Sunday, Clinton said the United States wanted to remain a solid supporter of Egypt's democracy after meeting with Egypt's top general.
Clinton spent about 2 hours with Field Marshal Mohamed Hussein Tantawi in Cairo discussing the sometimes-tense relationship between the military ruling council and the newly elected civilian government.
"We know that Egypt's future is up to the Egyptian people, but we want to be a good partner," Clinton told reporters after the meeting. "We want to support the democracy that has been achieved by the courage and sacrifice of the Egyptian people."
Clinton said she was encouraged to see Egypt renewing its relations with other African nations and reported progress in discussions between the two nations on debt relief and foreign assistance.
Clinton called on Tantawi a day after she met with President Mohamed Morsi, the Muslim Brotherhood candidate who was elected after President Hosni Mubarak was overthrown in 2010, CNN said.