The journalist was working for Iscanews, a news site managed by Azad University in Tehran, which also has other sites across Iran.
Iscanews confirmed the development, the Swiss ATS news agency reported.
The journalist had been sent to Lausanne to cover the negotiations with a photographer, German news agency DPA said.
The state secretariat for migration in Bern declined to comment on the situation.
It does not give information on particular cases because of privacy legislation, a spokeswoman for the secretariat told ATS.
The development occurred on the sidelines of negotiations that aimed to reach a deal on Iran's nuclear future by a Tuesday deadline.
An agreement between Iran and world powers is "doable" with "two or three" issues left to resolve, Tehran's lead negotiator said on Sunday, AFP reported.
"Getting to an accord is doable," Abbas Araqchi told reporters in Lausanne.
"Solutions have been found for numerous questions," he said.
"We are still working on two or three issues . . . the talks are in their final phase and are very difficult."
Araqchi said world powers would meet on Monday to discuss the issues.
US Secretary of State John Kerry and the German and French foreign ministers Frank-Walter Steinmeier and Laurent Fabius were due to sit down with Chinese foreign minister Wang Yi and EU foreign policy chief Federica Mogherini, as well as their Iranian counterpart Mohammad Javad Zarif.
They will be joined by Russian foreign minister Sergei Lavrov and his British counterpart Philip Hammond, who was the last to arrive in Lausanne, late on Sunday.