The Foreign and Commonwealth Office referred the PA news agency's request for comment to the Australian Department of Foreign Affairs and Trade, which has yet to respond.
It is thought that both women are now being kept at Evin prison in Tehran, the same jail where British-Iranian mother Nazanin Zaghari-Ratcliffe has been held on spying charges since 2016.
The latest arrests are unusual in that they involve Australians with no apparent family ties to Iran.
Johnson had previously come in for withering criticism for jeopardised the case of Nazanin Zaghari-Ratcliffe, a British-Iranian woman held in Tehran for sedition, by mischaracterising her job.
Ten-year terms are routinely given in Iran for spying charges.
The Australian Department of Foreign Affairs has confirmed it is providing assistance to three people detained in Iran. "Due to our privacy obligations, we will not comment further", a spokesperson said. They were reportedly keeping their followers on social media posted about the journey and it was the absence of the updates that initially prompted concern.
The latest round of detentions come as tensions between Iran and the West remain particularly high over a recent dispute over oil tankers, and the reintroduction of crippling economic sanctions on Iran after the U.S. withdrew from the 2015 nuclear deal last May.
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The British-Australian dual nationals are reportedly being held in prison in Tehran. European efforts led by France to save the accord are foundering, while the tit-for-tat seizing by United Kingdom and Iranian forces of oil tankers sparked a diplomatic storm between the two.
Dominic Raab, the Overseas Secretary, summoned the Iranian ambassador on Tuesday afternoon following experiences that the Adrian Darya 1, which was on the centre of a diplomatic disaster after being seized by Royal Marines in July, had delivered a cargo of crude oil to the Syrian port of Tartus.
Middle East Eye had reported exclusively on Friday that the supertanker had offloaded to a port in the country.
"It does sound extremely concerning and of course the UK government will do everything we can to support any UK British citizens who are caught in Iran", British business minister Andrea Leadsom told the UK's Sky News.
It warns "there is a risk that foreigners, including Australians, could be arbitrarily detained, or arrested".
Located in northern part of capital, Evin prison is notable for keeping political prisoners, dissidents and Iranians with dual nationality accused of plotting against the government.
"We can't guarantee access to consular services or legal representation if you're detained or arrested", the government's advice says.