Authorities are not sure who is responsible for the attack at the Grand Anwar Mosque but investigations are underway, said Information Minister Getachew Reda.
Despite deploying troops to Somalia to fight the al-Qaeda-linked militant group al-Shabaab, Ethiopia has largely avoided retaliatory attacks from the militants.
Al-Shabaab has previously targeted Kenya, Uganda and Djibouti who have also deployed troops to Somalia under the banner of the African Union to bolster the country's weak UN-backed government from an insurgency by the militants.
Ethiopian authorities have, however, recently jailed a number of Muslims on charges of terrorism and a conspiracy to establish an Islamic State in the country. A court sentenced 18 people to lengthy sentences in August.
Muslims have been protesting since 2011, accusing the government of interfering in their religion.