The activist, Emin Huseynov, has been sought by prosecutors on charges of "illegal entrepreneurship and tax evasion since last August," Azerbaijan's foreign ministry spokesman Hikmet Haciyev told AFP.
"A court ordered Huseynov's arrest, but he fled and is currently hiding at the Swiss embassy in Baku," he said.
The Swiss Federal Department for Foreign Affairs (FDFA) confirmed that "there is currently an Azerbaijani national at the Swiss embassy in Baku" but didn't reveal the identity of the person who has been sheltered at the embassy since August.
"Switzerland granted him authorization to stay (at the embassy) for humanitarian reasons," the FDFA spokeswoman, Ursina Schmitz, told AFP in an e-mailed comment.
"Switzerland has been negotiating with the Azerbaijani authorities and government to find a solution in the interests of this individual," Schmitz added.
The director of the Baku-based Institute for Reporters' Freedom and Safety, a media-rights group, Huseynov is known in Azerbaijan for his fierce criticism of President Ilham Aliyev's human rights record.
The oil-rich ex-Soviet republic often responds to dissent with tough measures.
Rights groups accuse Aliyev's government of consistently using spurious charges to jail regime critics and of stepping up a campaign to stifle opposition since his election for a third term in 2013.
Aliyev, 53, came to power in 2003 following an election seen as flawed by international observers.
He took over after the death of his father Heydar Aliyev, a former KGB officer and communist-era leader who had ruled newly independent Azerbaijan with an iron fist since 1993.
In annual report issued earlier this week, Reporters Without Borders ranked Azerbaijan 162nd out of 180 countries surveyed in its ranking of press freedom.
It singled out the country for having "Europe's biggest prison for news providers" with a number of journalists and bloggers behind bars and with media curbed by one-sided regulation.
On its website, Foreign Policy reported that Huseynov is married to an American servicewoman but that he was turned away from the US embassy in Baku after seeking refuge there.