The arrest of Gvaramia was made since the country's prime minister promised to punish political opponents who he believes are behind the protests that have been raging in the country since he decided to freeze talks on EU membership until 2028.
Opposition politicians who orchestrated the recent days' violence while hiding in their offices will not get away, said Prime Minister Irakli Kobachidze at a press conference on Tuesday.
Extensive protests against Kobachidze's EU decision have been ongoing in the country since Thursday.
The Ministry of the Interior later reported on Wednesday that seven people had been arrested by the police after searches at the opposition parties' offices and activists' homes. They are accused of having organized and led "group violence" in connection with the protests.
The suspects may risk up to nine years in prison, according to the ministry.
Activists have demanded a re-election in the autumn. Georgia went to the polls on October 26, but the result has not been recognized by the EU Parliament or the opposition, who claim electoral fraud. According to the official result, the ruling party Georgian Dream, which Irakli Kobachidze belongs to, received 89 of the parliament's 150 seats.
Georgia's President Salomé Zourabichvili is pro-Western and EU-friendly and has expressed support for the demonstrators in recent days.