Members of Egypt's military and police were chasing "terrorist elements" in the country's vast Western Desert when they came upon the tourists. Among the victims are people from Mexico and Egypt, the ministry said.
The attack happened Saturday within a so-called restricted area.
The tourist group was in cars that were not authorized for tours, and they did not have permits for the trip, MENA state news agency reported citing Egypt's tourism ministry.
An investigation is ongoing.
Two of those killed and at least five of those injured were Mexican nationals, Mexico's foreign ministry said. But the government is still in the process of identifying all of the victims.
The country's ambassador to Egypt, Jorge Alvarez Fuentes, spoke to five of the Mexicans who were hospitalized, according to a statement.
Mexican President Enrique Pena Nieto mourned the loss of his country's citizens in posts to Twitter.
"Mexico condemns these acts against our citizens and has demanded that the Egyptian government conduct an exhaustive investigation of what happened," he said.
The Mexican ambassador to Egypt is aiding the country's injured citizens who are hospitalized, Nieto said. He has called for the embassy to increase staff to help victims and their families.
Tourism and militants
Egypt's Western Desert draws tourists with spectacular landscapes such as the Great Sand Sea, which Egypt's tourism board advertises as "the world's third largest dune field." All terrain vehicles carry groups of sightseers up and over dunes and past rock formations whittled into aesthetic shapes by eons of wind-blown sand.
Tourists stop over at oases to enjoy rich desert culture and cuisine.
But the area, which is next to Libya, has also become attractive to insurgents since the fall of the government of former Libyan leader Moammar Gadhafi in 2011.
The border became porous allowing the unhindered transport of weapons, drugs and people to and from Egypt, according to The Washington Institute for Near East Policy, a think tank that specializes on U.S. diplomacy in the Middle East.
After Egypt's military deposed former Egyptian President Mohamed Morsy of the Muslim Brotherhood in 2013, Islamist militants stepped up attacks against military targets in the Western Desert.
A deadly attack on an Egyptian guard post at the oasis town of Farafra in July last year prompted the Egyptian military to launch a campaign against insurgents operating near Libya. Farafra is also a tourist destination.