Interior Minister Mohamed Abdi Gabose told the BBC the men had arrived in the territory by boat and then travelled overland to the border.
He said documents the men left behind suggest they belong to the Ogaden National Liberation Front (ONLF).
Somaliland has declared its independence from the rest of Somalia.
Its secession has not been internationally recognised but is far more stable than the rest of the country and in July held an election which saw a peaceful handover of power.
Mr Gabose said the armed group were surrounded in the mountainous region which borders Ethiopia and Djibouti.
The ONLF is fighting for the self-determination of ethnic Somalis in eastern Ethiopia, and has not yet commented on the allegations.
Eritrea has previously been accused of training ONLF rebels – charges it denies.
Eritrea and Ethiopia have a long-running border dispute.
Somaliland has previously helped the Ethiopian government in its fight against the ONLF.
