Local authorities have said Mount Nyiragongo could erupt once again with little warning.
The volcano, 10km (six miles) from Goma, spewed lava over the weekend, killing 32 people and leaving thousands homeless, the UN says.
Goma is a lakeside city where around 670,000 people live, according to UN estimates.
Ndima Kongba, the military governor of North Kivu province, ordered the evacuation of nearly a third of the city’s residents on Thursday. “Current data on seismicity and the deformation of the ground indicate the presence of magma under the urban area of Goma, with an extension under Lake Kivu,” Ndima said in a broadcasted public address.
“Right now we can’t rule out an eruption on land or under the lake, which could happen very soon and without warning,” he added. “The situation can change rapidly, and is being constantly monitored.”
Evacuation is necessary and should be done calmly and without rushing, he continued, saying that authorities had arranged transport towards Sake, around 20 kilometres west of Goma, in each of the ten districts of the city affected.
“People should take the bare minimum with them, to make sure everyone has a chance to get on,” he added.
The announcement was followed by the immediate departure of tens of thousands of people towards the southwest, in the direction of the Rwandan border.
Rwandan authorities are directing these people to a former refugee camp and a secondary school.
Many residents of Gisenyi itself have fled east, deeper into Rwanda, as earth tremors continue to shake the city. Rwandan authorities have reported earthquakes on Thursday reaching 4.9 magnitude.
Rivers of molten rock streamed from Mount Nyiragongo during its eruption on Saturday, setting houses and forest alight on the edges of Goma.