The incident occured outside the international stadium in the heart of the capital, during prayers.
Ethiopian police used tear gas to disperse young Muslims in Addis Ababa during prayers to mark the end of Ramadan in the capital.
The incident occurred outside the international stadium in the heart of the city, where prayers were scheduled to celebrate the Eid al-Fitr holiday at the end of the Muslim holy month.
Unable to gain access because the stadium was full, some worshippers began to pray outside, in Meskel Square.
A member of the Addis Ababa High Council of Islamic Affairs told the AFP news agency that the cause of the confrontation was unclear.
However, tensions have been high in the country after the deaths of at least 20 people last month in Gondar, a town in the northwestern region of Amhara, when Muslims were attacked by heavily-armed “extremist Christians”, according to local Muslim groups.
A policeman fired tear gas at the crowd but “it was unintentional,” the official said, quoting volunteers at the site.
“The policeman was evacuated by other policemen, but people were shocked and some started to chant slogans… the situation became uncontrollable
Addis Ababa police issued a statement saying “a riot” had been caused by a “few individuals” and led to property damage, but order had now been restored.
“[The] police are calling on the community to remain calm,” it said.
Stone-throwing demonstrators also smashed windows at a national museum on Meskel Square before calm was restored, reports said
The Addis Ababa official told AFP that Eid al-Fitr prayers had taken place in the city every year since the end of the Marxist-military Derg government in 1991.
“This is the first time such incidents happen,” the official said, adding that the Muslims attending the ceremonies were unarmed, as everyone was searched by police before they entered the venue.