IRNA did not specify the identity of the suspects or say how many were arrested.
But the agency said that Israeli intelligence agents tried “to approach” an employee at Fordo after “recruiting” one of his neighbours, in order to gain information about a centrifuge used at the facility.
Iran has repeatedly accused US or Israeli agents of spying on and attempting 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 had arrested several “spies” in Bushehr province, where the country’s sole nuclear plant is based.
In 2020, Tehran accused Israel of being responsible for the killing of top Iranian nuclear scientist Mohsen Fakhrizadeh in an attack near Tehran.
The following year it claimed Israel was behind a “small explosion” that hit its Natanz uranium enrichment plant.
Monday’s allegations came on the eve of a visit to Moscow by Foreign Minister Hossein Amir-Abdollahian for nuclear talks.
Negotiations in Vienna to revive Iran’s 2015 nuclear deal with world powers had lately made progress, but they were halted after Russia earlier this month demanded guarantees that Western sanctions imposed following 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 unilaterally withdrew from the accord in 2018 under then-president Donald Trump and imposed tough economic sanctions on different sectors, including oil exports.
Iran hit back with several actions, including resuming enrichment at Fordo.