The Natanz nuclear site, which is close to the central city of Esfahan, is subject to frequent inspections by the UN's nuclear watchdog, the International Atomic Energy Agency, and was the target of a Stuxnet computer virus attack in June 2010.
The Natanz nuclear facility is located near a major highway, and is generally recognized as Iran's central facility for uranium enrichment with more than 19,000 gas centrifuges now operational and almost half of them being fed with uranium hexafluoride, a compound used in the process of enriching uranium, which produces fuel for nuclear reactors and nuclear weapons.
The spokesman said that the accident occurred at a construction site and did not impact the uranium enrichment facility in operation.
"The incident did not cause any casualties and did not damage the current activities of this complex", Kamalvandi was quoted as saying by several Iranian media outlets including the state-run IRNA news agency.
He did not give any details on the nature of the reported accident.
Iran is investigating the cause of a fire at an under-construction building near its biggest uranium enrichment facility.
Kamalvandi was further quoted as saying that the complex is now inactive and there is no risk of radioactive pollution.
Some experts did not rule out possibility of sabotage given the importance of the Natanz nuclear site.
A "pre-fabricated steel framework" which was part of a structure being built on an open area of the site was left broken and damaged, Kamalvandi said, adding "there is no reason to worry". Iran began expanding its enrichment programme after the United States unilaterally withdrew from the 2015 nuclear deal, which curbed the Islamic Republic's nuclear ambitions in exchange for the lifting of sanctions.
Iran restarted enriching uranium at Natanz last September.
Iran says there has been an "incident" at one of its nuclear facilities.
There was no immediate comment from the International Atomic Energy Agency in Vienna.