Gen Bruno Mandevu said the clash had occurred in the Virunga National Park, on Congolese territory - a claim Rwanda denied.
He said the Congolese troops initially thought they were fighting one of the many rebel groups active in the area.
Some fear these clashes could increase tensions between the countries, which have a troubled history.
Rwanda twice invaded its much-larger neighbour in the 1990s.
Rwandan army spokesman Col Innocent Munyengango confirmed the clashes to the BBC Great Lakes service and said there had been no Rwandan casualties.
"Congolese encroached on our base and attacked us. Our soldiers had to defend themselves," he said.
Eastern Democratic Republic of Congo, across the border with Rwanda, remains deeply unstable.
Aid agencies are warning about violence in the north-eastern Ituri province, where the United Nations children's agency, Unicef, says more than 46,000 children are on the run.
The BBC's Catherine Byaruhanga has seen burnt and abandoned villages in the province where people from the Hema and Lendu ethnic groups have been fighting for control of land.
Earlier this week, the Norwegian Refugee Council, a humanitarian NGO, warned that the crisis in DR Congo was at a deadly tipping point.
In the past two years, more people have been displaced in DR Congo than any other country. A total of 4.5 million people need assistance.