Penner, who tweeted in favour of the Madhes movement and also on the arrest of veteran journalist Kanak Mani Dixit, has been charged with spreading messages through social media, disturbing social harmony in the country.
A Home Ministry spokesperson said Penner has been asked to leave the country within 48 hours and if he did not obey the government's order he will be put into the prison.
Penner, 37, who has been working in Nepal for about four years, was arrested from Lalitpur district yesterday.
Madhesis, mostly of Indian origin, have been demanding that Nepal's Constitution be amended to include their concerns over inadequate political representation and redrawing of federal boundaries.
They had enforced months-long blockade of Nepal's all trading points with India, creating huge shortage of essential commodities in the country.
Penner recently tweeted criticism of Nepal's anti-graft watchdog for its handling of arrest of journalist Dixit.