The centre housed patients suspected of having the deadly viral disease before the confirmed cases are transferred to an isolation center.
"The protesters have attacked the Ebola centre in the town. This is serious because the epidemic can spread," Matthieu Kamble, a resident, told Al Jazeera by telephone.
The demonstrators were unhappy with the electoral commission (CENI) after it delayed Sunday's election in three DRC cities.
On Wednesday, CENI said voting in Beni and Butembo in the eastern North Kivu province and Yumbi in western Bandundu province will take place in March next year instead.
The commission said it delayed the poll in North Kivu because of the ongoing Ebola outbreak in the region, the second-worst in history.
The latest outbreak, which started in May 2018, has left more than 320 people dead.
'We have to vote'
"The electoral commission is responsible for what's happening. We don't accept the delay, we have to vote," Kambale said.
Another resident, Justin Safari, said the situation in the city will not change unless people are allowed to cast their ballot.
DRC delays vote in three cities (2:24)
"Delaying over the Ebola outbreak is not good enough a reason. They can't use it to leave us behind while other Congolese vote on Sunday. It doesn't make any sense," Safari said.
Residents in Beni told Al Jazeera that security forces used tear gas and fired in the air to disperse protesters, who burned tires and blocked roads to express anger at their exclusion from the polls.
"Protesters blocked the main road and destroyed the Ebola centre. They are chasing the volunteers fighting the disease. Nobody wants to accept an election delay here," Kizito Bin Hangi, president of Beni Civil Society, told Al Jazeera.
The DRC was scheduled to have its election in 2016, but the electoral body kept delaying, citing a lack of resources to hold the polls in the vast country which is roughly five times the size of France.
CENI scheduled the vote for December 23, but that again was extended by a week after voting machines were destroyed in a fire at the electoral body's main warehouse in the capital, Kinshasa.
More than 46 million Congolese are registered to take part in the polls.
Twenty-one candidates are competing to succeed President Joseph Kabila, who is stepping down after more than 17 years in power.
The DRC has never had a peaceful transfer of power since the mineral-rich country gained independence from Belgium in 1960.