The incident appears to be the first of its kind since Tehran's landmark deal with major powers was struck in 2015, imposing restrictions on Iran's nuclear activities in exchange for the lifting of international sanctions.
It comes at a time of heightened frictions between Iran and the West, with Tehran breaching the deal's restrictions step-by-step in response to Washington's withdrawal from the deal and renewed sanctions. The IAEA is also in transition, with a new chief due to take office next month.
The issue is due to be discussed at a meeting of the IAEA's 35-nation Board of Governors on Thursday convened at short notice to discuss "two safeguards matters" not specified in the agenda, which was circulated on Monday.
"The agency wants to show how seriously they are taking this. It is a potentially damaging precedent," one Western official said.
Three diplomats familiar with the agency's work said the female inspector had her travel documents taken, and two said she was briefly held while working in Iran.
One of the diplomats said the incident occurred at Iran's enrichment site at Natanz last week. Another one also said the incident took place at Natanz.
"There is a real concern that it will harm how (the IAEA) carry out their inspections in the future," a European diplomat said.
The nuclear deal, which the IAEA is policing, allows for 130-150 inspectors from the agency designated for Iran.
An IAEA spokesman and Iran's ambassador to the agency declined to comment.
The other matter due to be discussed on Thursday is Iran's less than full cooperation with the IAEA in explaining how traces of uranium were found at a site in Tehran that Israel has called a "secret atomic warehouse", diplomats said.
Although the IAEA has declined to confirm officially that it found uranium traces at the site, which Iran has said was a carpet-cleaning facility, it told Iran in September that "time is of the essence" in answering its questions, and it reported an improvement in Iran's cooperation last month.