However, the operating system at the Bushehr plant - due to go online in a few weeks - has not been harmed, project manager Mahmoud Jafari said.
The Stuxnet worm is capable of seizing control of industrial plants.
Some Western experts say its complexity suggests it could only have been created by a "nation state".
It is the first sign that Stuxnet, which targets systems made by the German company Siemens, has reached equipment linked to Iran's nuclear programme.
The West fears Iran's ultimate goal is to build nuclear weapons. Iran says its programme is aimed solely at peaceful energy use.
Stuxnet is tailored to target weaknesses in Siemens systems used to manage water supplies, oil rigs, power plants and other utilities.
'Electronic war'
The fact that Stuxnet has now been detected on the personal computers of staff will have no impact on plans to make the Bushehr plant operational next month, Mr Jafari said.
A team is now trying to remove the malicious software, or malware, from several affected computers, he told IRNA.
It is believed to be the first-known worm designed to target major infrastructure facilities.
"An electronic war has been launched against Iran", Mahmoud Liayi, head of the information technology council at the ministry of industries, told the state-run Iran Daily newspaper.
A working group of experts met last week to discuss ways of fighting the worm, which Mr Liayi said has now infected about 30,000 IP addresses in Iran.
