A video widely circulated on Congolese social media showed a missile flying towards an airborne military jet before exploding near the plane, which continued to fly.
Congo has refuted Rwanda's claim that the plane was in Rwandan airspace, the latest spat between the two countries strained by a rebel war.
"The Rwandan shots were directed at a Congolese aircraft flying within Congolese territory," it said in a statement, adding the jet landed safely in the province capital Goma.
It called Rwanda's action a "deliberate act of aggression that amounts to an act of war" intended at sabotaging a peace accord to cease the M23 rebel group's onslaught.
The Rwandan government previously stated that Rwandan military shot on the plane after it breached Rwandan airspace around Rubavu - the same region as prior alleged violations - "prompting the government to take defensive measures."
"Rwanda requests that the DRC cease this attack," said government spokesman Yolande Makolo in a statement.
Rwanda has been accused by UN experts and Western countries of supporting the M23 in eastern Congo, which took numerous towns and villages in fresh fighting last year. Rwanda has categorically denied any connection.
Regional authorities reached a deal in November under which the Tutsi-led group was supposed to withdraw from newly acquired locations by January 15 as part of attempts to cease the war, which has displaced at least 450,000 people.
Last Monday, Congolese President Felix Tshisekedi stated that the rebels had not completely retreated from certain districts.
In December, Rwanda reported that another Congolese fighter plane had briefly breached its airspace.
In November, an unarmed Congolese warplane temporarily landed at a Rwandan airstrip while on a surveillance mission near the border, which Congo said was an accident.