The government said three police officers and one civilian were killed.
The violence is believed to have started after the attempted arrests by government troops of leaders of the Amhara ethnic group.
Al Jazeera could not independently verify the reports.
“The government is saying they were trying to arrest people linked to a terrorist organisation. We’ve spoken to some people who say tourists have been moved out of the city to safe areas. The city is under lockdown,” Al Jazeera’s Charles Stratford, reporting from the capital Addis Ababa, said.
Ethiopia has seen other protests this year in Gondar and elsewhere, Stratford said. Human rights organisations say that 300 people were killed during protests by the largest ethnic group, the Oromo.
Images posted online and said to be from Gondar showed burned-out vehicles and armed men firing guns in the air as hundreds of other people cheered them on.
The Amhara are the second largest ethnic group in the country.
“They say that they are being ignored by the government – the government that they alleged is dominated by other ethnic groups from the north,” Stratford said.
The violence prompted the US embassy in Ethiopia to issue a temporary advisory warning against travel to the city centre of Gondar and areas where “violent demonstrations” have been reported.
“The embassy recommends all US citizens travelling to or resident in the Gondar area evaluate their personal level of safety and to avoid demonstrations or large gatherings,” the advisory issued on Wednesday said.