The suspects "planned on sabotaging the Fordo facility and were arrested by the intelligence services of the Revolutionary Guards", Irna news agency said.
Fordo is an underground uranium enrichment centre outside the central city of Qom, about 180 kilometres south of Tehran.
Irna did not specify the identity of the suspects or say how many were arrested.
But it said that Israeli intelligence agents tried "to approach" an employee at Fordo, after "recruiting" one of his neighbours, to gain information about a centrifuge used at the complex.
Iran has repeatedly accused US or Israeli agents of spying on and trying to sabotage its nuclear programme, including by killing scientists.
In August 2012, saboteurs blew up power lines supplying Fordo.
Two years later, Iran said it arrested "spies" in Bushehr province, which contains the country's sole nuclear plant.
In 2020, Tehran accused Israel of killing top Iranian nuclear scientist Mohsen Fakhrizadeh in an attack near the capital.
The following year it claimed Israel was behind a "small explosion" at its Natanz uranium enrichment plant.
Monday's allegations came on the eve of a visit to Moscow by Foreign Minister Hossein Amirabdollahian for nuclear talks.
Talks in Vienna to revive Iran's 2015 nuclear deal with world powers have lately made progress.
But they were halted after Russia this month demanded guarantees that western sanctions imposed after its invasion of Ukraine would not damage its trade with Iran.
The 2105 deal gave Iran sanctions relief in exchange for curbs on its nuclear programme.
But the US withdrew from the accord in 2018 under president Donald Trump and imposed tough economic sanctions on different sectors, including oil exports.
Iran hit back by breaching parts of the deal, including by resuming enrichment at Fordo.