The tourists were travelling in four vehicles that entered a restricted zone in the Wahat area of the Western Desert, a ministry statement said.
Ten Mexicans and Egyptians were also injured and are being treated in a local hospital.
The ministry said it had formed a team to investigate the incident.
Mexico’s President Enrique Pena Nieto condemned the incident and said he had “demanded an exhaustive investigation by the Egyptian government”.
The Mexican foreign ministry confirmed that at least two of its nationals had been killed and said it was working to confirm the identities of the other victims.
In a statement, the foreign ministry said Mexico’s ambassador in Egypt, Jorge Alvarez Fuentes, had visited the local hospital and spoken to five Mexicans who were in a stable condition.
The statement from Egypt’s interior ministry said the four vehicles the tourists were travelling in were “mistakenly dealt with” during a joint military police and armed forces operation.
It said the incident happened on September 13 in an area that “was off limits to foreign tourists”, but it did not give an exact location.
The group of tourists was preparing to camp out in the vast Western Desert when they came under fire.
According to the interior ministry’s statement, the security forces were pursuing Islamic militants in the desert, and targeted the four vehicles which were away from the main road with an Apache helicopter, which shot and hit the four vehicles.
The tour company transporting the tourists “did not have permits and did not inform authorities”, tourism ministry spokesman Rasha Azaz told the Associated Press.
The vast Western Desert area is popular with foreign sightseers, but is also attractive to militants.
The area – which borders Libya – is a gateway to the long border and weapons are available on the other side.
On September 13, ISIS in Egypt claimed it had “resisted a military operation” in the desert.
A group claiming to be affiliated with ISIS also said on the same day that it was present in Farafra.
The insurgency in Egypt gathered momentum after the army overthrew Islamist President Mohamed Morsi of the Muslim Brotherhood in mid-2013 following protests against his rule.
The government says hundreds of police and soldiers have been killed, many of them in attacks claimed by ISIS’ Sinai Province affiliate.
Up until recently most of the fighting has taken place in the Sinai Peninsula with occasional attacks taking place in Cairo and other cities.
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