At least five deaths have been reported while people were evacuating and fleeing to safety but officials are yet confirm those reports.
Houses were destroyed in the city due to the disaster which occurred 10km (six miles) from Goma.
Rwandan authorities said about 3,000 people had officially crossed from Goma.
Tom Peyre-Costa, from the Norwegian Refugee Council in Goma, told the BBC how the scene had unfolded.
“The lava was pretty slow, like, one kilometre per hour, but it didn’t stop…. It started burning the houses,” he said, adding that humanitarian organisations were already trying to address people’s needs.
Residents have also been speaking a day after the disaster, sharing their stories of the moment the eruption occurred.
One Goma resident, Richard Bahati was quoted by the BBC as saying that he heard screaming and became extremely worried as he saw the sky reddening outside.
“I lived through the problem with this volcano in 2002. The volcano devastated all our homes and possessions,” he said.
The last time such an eruption occurred was in 2002 and it killed 250 people and rendered 120,000 homeless.