It did not say whether they were still under arrest, with Britain responding that the reports were "completely false".
"These spies were taking earth samples in Iran's central desert where the Revolutionary Guards' aerospace missile exercises were conducted," state TV said.
Video showed what it said was footage of Giles Whitaker and his family in central Iran where the British diplomat appeared to be taking ground samples.
The broadcast said it was near an area where a missile test was taking place.
"Whitaker was expelled from the city after apologising," the TV report said.
However, a spokesman for Britain's Foreign Office said: "Reports of the arrest of a British diplomat in Iran are completely false."
Samuel Heath, UK spokesman to the United States, tweeted: "He (Whitaker) is not even posted in Iran anymore!".
One of those detained was identified by state TV as the husband of Austria's cultural attache in Iran. Austrian officials were not immediately available to comment on the matter.
The broadcast also showed a picture of a third foreigner, identified as Maciej Walczak, a university professor from Poland, who it said was visiting Iran as a tourist.
The TV report ran footage allegedly showing Walczak and three colleagues collecting earth samples in another area after visiting Iran on a scientific exchange program.
It said their sample collection coincided with a missile test in Iran's southern Kerman province.
Iran's elite Revolutionary Guards have arrested dozens of dual nationals and foreigners in recent years, mostly on espionage and security-related charges.
Rights groups have accused the Islamic Republic of trying to win concessions from other countries through arrests on security charges that may have been trumped up.
Tehran denies arresting people for political reasons.
