The tourists were travelling in four vehicles that entered a restricted zone in the Wahat area of the Western Desert, the ministry said. Sources said eight of those killed were Mexicans.
Ten Mexicans and Egyptians were also injured.
Egypt has been battling Islamist militants for years.
Attacks on army and police, mainly in the Sinai peninsula, have escalated since Islamist President Mohammed Morsi was ousted in 2013.
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 Sunday in an area that "was off limits to foreign tourists", but it did not give an exact location.
Survivors said they suffered an "aerial attack" after stopping for a meal, according to Mexican Foreign Minister Claudia Ruiz Massieu. She could only confirm that two Mexican nationals had been killed.
Mexico's President Enrique Pena Nieto condemned the incident and demanded an "exhaustive" investigation by Egypt.
The disastrous shooting up by Egyptian security forces of a tourist convoy in the Western Desert is yet another sign of growing instability in the Arab world's most populous country.
Egypt's western oases are spectacularly beautiful, hence their popularity with adventure tourists.
But since the Arab Spring upheavals of 2011, security along Egypt's border with Libya has deteriorated as the Islamist insurgency has grown across the country. Vast stretches of both the Sinai Peninsula and the Western Desert are now too dangerous for Westerners to visit.
Last month IS militants beheaded a Croatian engineer they had kidnapped not far from Cairo. Now the possibility of being mistakenly shot at by the authorities, as well as being kidnapped by militants, will further damage Egypt's much depleted tourism revenues.
Egyptian officials say the tourists were in a no-go zone – and had not liaised with the authorities.
But a local tour guide has denied that, saying the group was in an unrestricted area, on top of sand dunes, trying to get a bird's eye view.
Another local source – who claims to have spoken to a driver who survived the incident – told the BBC the tourists even had a police escort.
He said the safari was organised by a local hotel which co-ordinated with the security forces.
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 vast Western Desert area is popular with foreign sightseers, but is also attractive to militants, reports the BBC's Orla Guerin in Cairo.
The area – which borders Libya – is a gateway to the long border and weapons are available on the other side, our correspondent adds.
On Sunday, the Islamic State group (IS) claimed it had "resisted a military operation" in the desert.
A group claiming to be affiliated with IS also said on Sunday that it was present in Farafra.
The insurgency in Egypt gathered momentum after the army overthrew President Mohammed Morsi of the Muslim Brotherhood in 2013 following protests against his rule.
Hundreds of police and soldiers have been killed, many of them in attacks claimed by IS's Sinai Province affiliate.
Until recently most of the fighting has taken place in the Sinai Peninsula with occasional attacks taking place in Cairo and other cities.
In July, Egypt vowed to rid the peninsula of militants after clashes with IS fighters there killed more than 100 people.