The ministry said three drones were involved but there were no casualties.
One drone was destroyed by air defence systems and two were caught by "defence traps", causing minor damage to a building, the ministry added.
The extent of damage to the site has not been confirmed by the BBC, and there has been no immediate claim of responsibility.
Iran's foreign minister, Hossein Amir-Abdollahian, said the "cowardly" incident was an attempt to destabilise the country.
But he added that the incident would not impact Iran's "determination and intention regarding the peaceful nuclear progress".
It comes amid heightened tensions over Iran's nuclear programme and its supply of arms to Russia's war in Ukraine.
The country has also been wracked by internal turmoil in recent months, spurred by the death of a woman who was detained for violating Iran's strict dress code.
In a statement to Iranian state media, the defence ministry said the drone strike happened on Saturday night at around 23:30 local time (20:00 GMT).
Local authorities did not comment on activities at the site, but called it a "workshop". The IRNA news agency said the strike had targeted "an ammunition manufacturing plant".
Isfahan province is home to a large air base and several nuclear sites, including Natanz, which is at the centre of Iran's uranium enrichment programme.
In a separate incident on Saturday, the IRNA new agency reported a fire broke out at an oil facility near the north-western city of Tabriz. No details about the cause have been revealed.
In recent years, there have been a number of explosions, fires and cyber attacks on Iranian military, nuclear and industrial facilities.
After Iran accused Israel of sabotaging the key nuclear facility near the city of Natanz in 2021, Israel's defence chief said the country's operations in the region "are not hidden from the eyes of the enemy".
And in 2020 Iran alleged that Israel was behind the assassination one of its top nuclear scientists, Mohsen Fakhrizadeh.