The global human rights group Amnesty International fears for the safety of two Ethiopian teachers detained "incommunicado".
Wasihun Melese and Anteneh Getnet, members of EI affiliate the Ethiopian Teachers' Association (ETA), are "at risk of torture, ill-treatment or disappearance", said Amnesty.
The ETA has been vocal in its criticism of the government's education policies, and Amnesty said their arrests may be linked to the complaints.
The group said: "These new arrests may be a response by the Ethiopian authorities to a complaint lodged by the ETA and the global union federation Education International... citing government interference with ETA activities and intimidation of ETA members."
Numerous ETA activists have been arrested since May 2005 and the Ethiopian government has made several attempts to replace the union with a pro-government organisation with the same name, said Amnesty.
Some were detained in massive crackdowns on dissent following eruptions of violence that killed scores of people after that month's disputed general election.