Violence in DRC has been spiralling, with reports of summary executions being carried out by the rebel M23 group and growing numbers of refugees.
The UK suspended the last tranche of £16 million of aid in July after an interim UN report highlighted Rwanda's role in backing the insurgents.
Ms Greening's predecessor, Andrew Mitchell, controversially reinstated the payments on his last day in the job. He authorised £8 million as direct support to the government, and diverted the other half to specific development programmes.
In a damning report, an influential group of MPs insisted they "did not understand" why Mr Mitchell concluded the state was no longer backing the M23.
Downing Street denied it had been a mistake to reinstate aid in September. Asked if David Cameron stood by his previous praise of Rwanda as a "success story", the PM's spokesman said: "There has been progress made in that country. This decision is about aid spending." Mr Cameron raised concerns with Mr Kagame when he spoke to him by telephone a few weeks ago, he said.
Ms Greening pointed to fresh evidence presented by UN experts earlier this month about Rwanda's role in fuelling the conflict, describing it as "credible and compelling". She also said Britain would provide a further £18 million of immediate humanitarian support in DRC, including emergency food for 100,000 people, clean water and education.
TaxPayers' Alliance campaign manager Robert Oxley said: "It's appalling that British taxpayers' money has gone directly to a government involved in a proxy war that has brought untold misery to hundreds of thousands of people. This announcement leaves a huge question mark over why DfID, and specifically Andrew Mitchell, reinstated the aid programme to the Rwandan government which was fanning the flames of conflict in DRC."
Shadow international development secretary Ivan Lewis welcomed the "belated" move to suspend aid, and accused Mr Mitchell of a "serious misjudgment". He said: "We never accused Andrew Mitchell of being a rogue minister. However, recent developments have demonstrated his decision to unilaterally reinstate budget support to the government of Rwanda was a serious misjudgment with grave consequences for stability in eastern DRC and Britain's credibility."