The latest round of trouble has been sparked by the deaths of at least 55 people after a stampede at a religious festival that turned into an anti-government protest.
Three days of national mourning followed the deaths on Sunday. The opposition, which puts the death toll much higher, blames the action of security forces for causing panic.
Information Minister Getachew Reda told the BBC that the continued violence was the work of organised criminals rather than being part of anti-government protests.
He said that the people causing the damage have been arriving at the scene on motorbikes carrying petrol bombs.
Leaders from the Inter-religious Council of Ethiopia have appealed for calm and a national dialogue.