"Belgium has suspended its military cooperation with Kigali," said Reynders on Twitter.
"We will not train soldiers who could contribute to the destabilisation" of Congo, he told Belga news agency.
Belgium's decision came after a UN expert panel accused Rwanda of arming and supporting M23 rebels, an ethnic Tutsi rebel movement unsuccessfully integrated into the Congolese military under a 2009 peace deal.
Reynders noted that EU foreign ministers would examine sanctions against Kigali during their upcoming meeting on November 19.
The European Union suspended all aid to the Rwanda at the end of September.
Belgium and Rwanda's military partnership, concluded in 2004, mainly included the training of Rwandan troops, research and health.
Two Belgian soldiers were sent in May to a military hospital in Kigali for eight weeks to assist specialists on tropical medicine, Belga said.
A final training session was meant to be carried out in Belgium in 2012, but it has now been scrapped. No new activities with Rwanda have been planed for 2013, the news agency reported, quoting Defence Minister Peter De Crem.
Last month, Belgium abstained during a vote on the election of Rwanda to membership of the Security Council for 2013-2014.
"We abstained to make a point," said Reynders.
"It is obviously not our priority to see a country implicated in such a case obtain a seat on the Security Council," he said.
Rwanda won the non-permanent seat for two years with 148 votes from 193 member states of the General Assembly.