The Fars News Agency, one of Iran's biggest, stopped running articles before noon local time (0730 GMT) following the order from a supervisory media board.
The agency had carried a report on Sunday evening citing an informed source as saying the cabinet that day had discussed the possibility of replacing Central Bank Governor Tahmasb Mazaheri.
"Last night we received a call from the presidential office ordering us to deny the report about Mazaheri's dismissal and we said we will not do it until we get a written order," the editor told Reuters, declining to be named.
"This morning the board closed our agency for three days," the editor said.
The Ministry of Culture and Islamic Guidance said Fars had published an "untruthful piece of news which in addition to conveying dispute and division between officials led to agitation and instability in the economic activities arena."
It added in a statement carried by the ISNA news agency: "Fars news agency is obliged to cease any news activity ... when the decision by the supervisory board was communicated to the news agency's director."
Iranian media have speculated about Mazaheri's imminent departure from the post following reports of disagreement with President Mahmoud Ahmadinejad over interest rates in the world's fourth-largest oil producer.
Ahmadinejad, who came to power in 2005 on a pledge to share out Iran's oil wealth more fairly, has come under mounting criticism from parliament, the media and the public over failure to rein in inflation now running at around 24 per cent annually.
Mazaheri has publicly criticised Ahmadinejad over interest rate policy. Ahmadinejad has called for low interest rates and said those who oppose cutting rates should "step aside".
Although Iran says it allows free speech, journalists say they have to tread carefully between a growing number of "red lines" to avoid being closed down.
Since 2000, Iran has closed more than 100 publications, accusing many of being "pawns of the West". Many subsequently reopened under different names.