The postponement was reported on Friday night by Reuters which quoted a diplomat close to the UN nuclear watchdog as saying the Tehran's government's motive is unclear.
"The Iranians have postponed the inspections until the second half of April, possibly the end of April," the diplomat said after a meeting of the governing board of the International Atomic Energy Agency (IAEA).
An IAEA spokeswoman refused to comment when contacted for confirmation.
Earlier, the Iranian ambassador to the IAEA Pirooz Hosseini said his country had put back the mission, scheduled to start this week, "due to the approach of the Iranian New Year."
He did not give a new date for the inspections.
The postponement of over a month has the IAEA thinking that if the Iranians "really had nothing to hide, this is fully against their interests."
The diplomat said this was giving those like the United States who accuse Iran of hiding a nuclear weapons programme "a big pile of ammunition with this move."
The postponement means that the IAEA inspectors will be in Iran "really only a month" ahead of a June board meeting that is to review the Iran situation, based on an IAEA report to be written in May.
The inspectors will have "not enough time" now to get a full report to the June board.
The diplomat said maybe Iran "felt the agency's inspectors were coming too close to them or wanted to show some political muscle of their own to defy those countries casting strong-worded resolutions condemning them."