"He is a criminal, and he definitely will have his day in court," government spokesperson Getachew Reda told AFP.
Andargachew Tsige, secretary general of Ginbot 7 - labelled a terrorist organisation under Ethiopian law - was arrested while transiting through the airport of Yemen's capital Sanaa last week, according to a statement from the group.
Yemen's National Security said he was held because his name was "on a list", but giving no further details.
Getachew said it would be "the right thing" if Yemen extradited Andargachew, accusing him of plotting terror attacks in Ethiopia.
"He's the head of a terrorist organisation who has been flaunting his leadership for terror operations inside Ethiopia," he said.
But Ginbot 7 said Andargachew was detained illegally and called for his release.
"The Yemeni government doesn't have any right to detain Andargachew, even for an hour," it said in a statement.
The US-based Ginbot 7 says it is fighting for democracy and freedom in Ethiopia, and has called for the overthrow of the ruling party.
The group vowed to seek retribution if Andargachew, who they called a "freedom fighter", is extradited to Ethiopia.
"If Andargachew is transferred into the custody of the Ethiopian government, if his life and physical wellbeing is threatened, we will avenge," it warned, without giving further details.
In 2012 several people were convicted for having links to Ginbot 7, including journalist Eskinder Nega and opposition leader Andualem Arage, who were handed heavy sentences.
The group's leader, former Addis Ababa mayor Berhanu Nega, lives in exile in the US.
Rights groups have accused Ethiopia of using the anti-terrorism legislation to silence dissent and jail critics, calling the legislation vague and over-reaching.