In a statement at a special meeting of the International Atomic Agency (IAEA) on Thursday, an EU representative expressed deep concern while a US envoy said Tehran's holding of the inspector was an "outrageous provocation".
Tehran said it blocked the IAEA inspector from visiting the plant last week after she triggered an alarm at the gate to the Natanz facility.
The state-run IRNA news agency, citing Iran's atomic agency, said the woman was stopped "due to concerns over carrying suspicious materials".
It did not specify what the product was, but said the inspector later left Iran without completing her visit.
The incident involving an IAEA inspector appeared to be the first of its kind since Tehran's landmark deal with major powers in 2015, which imposed curbs on its uranium enrichment programme in exchange for the lifting of international sanctions.
The landmark accord grants the IAEA wide-ranging inspection powers, including daily access to Iran's vast nuclear enrichment facilities at Natanz and Fordow.
The EU, in its statement, said it was "deeply concerned by the incident concerning one IAEA inspector".
"We understand that the incident was resolved and call upon Iran to ensure that no such incidents occur in the future," the statement said.
Reiterating the EU's "full confidence in the inspectorate's professionalism and impartiality", the statement called "upon Iran to ensure that IAEA inspectors can perform their duties in line with its legally binding safeguards agreement".
Jackie Wolcott, US ambassador to the IAEA, also slammed Iran's move.
"The detention of an IAEA inspector in Iran is an outrageous provocation. All Board members need to make clear now and going forward that such actions are completely unacceptable, will not be tolerated, and must have consequences."
Iran is also expected to address its decision to block the inspector at Thursday's IAEA meeting in Vienna.
The incident comes as Tehran scaled back compliance with the nuclear accord, following the US's decision last year to abandon the agreement and reimpose punishing sanctions against Iran.
The phased suspension of Iran's obligations under the deal is aimed at pressuring the remaining European signatories to the deal - the United Kingdom, France and Germany - to deliver on the accord's promised economic benefits and shield Iran's economy from the punishing US sanctions.