"The M23 must withdraw their forces immediately and allow legitimate government control to be restored. The cessation of hostilities and the protection of civilians is paramount," he said in a statement.
The International Crisis Group, an independent anti-conflict non-profit group, warned that the fall of Goma could lead to serious human rights abuses against civilians. The settling of scores or even extrajudicial killing of members of the authorities and civil society activists who have opposed M23 could fuel further violence, it said.
The unrest could also spread to neighboring communities and "relaunch open warfare between the DRC and Rwanda," the group said on its website.
The United Nations and some donor countries have accused neighboring Rwanda of backing the M23 rebel group by providing it with arms, support and even soldiers.
Rwandan President Paul Kagame has repeatedly denied the allegation, and Mushikiwabo said Tuesday Rwanda has moved "way past" the accusations.
Rwanda will not engage in any talks with M23, Mushikiwabo said. "Our interlocutor is the government of the DRC," she said.
Mushikiwabo said Rwanda would close the border crossing if asked to by the Congolese government, but that such a move could have humanitarian consequences.
Tens of thousands of Congolese, already displaced by previous rounds of fighting in the volatile region, have fled camps around the edges of Goma, according to UNICEF and the medical charity Doctors Without Borders.